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  Subjects -> ENGINEERING (Total: 2070 journals)
    - CHEMICAL ENGINEERING (171 journals)
    - CIVIL ENGINEERING (161 journals)
    - ELECTRICAL ENGINEERING (88 journals)
    - ENGINEERING (1148 journals)
    - ENGINEERING MECHANICS AND MATERIALS (320 journals)
    - HYDRAULIC ENGINEERING (52 journals)
    - INDUSTRIAL ENGINEERING (52 journals)
    - MECHANICAL ENGINEERING (78 journals)

ENGINEERING (1148 journals)            First | 2 3 4 5 6 7 8 9 | Last

International Journal of Information Acquisition     Hybrid Journal   (Followers: 1)
International Journal of Innovation and Applied Studies     Open Access   (Followers: 2)
International Journal of Innovation Science     Full-text available via subscription   (Followers: 6)
International Journal of Integrated Engineering     Open Access   (Followers: 1)
International Journal of Intelligent Engineering Informatics     Hybrid Journal  
International Journal of Intelligent Systems and Applications in Engineering     Open Access  
International Journal of Lifecycle Performance Engineering     Hybrid Journal   (Followers: 1)
International Journal of Machine Tools and Manufacture     Hybrid Journal   (Followers: 5)
International Journal of Manufacturing Research     Hybrid Journal   (Followers: 5)
International Journal of Manufacturing Technology and Management     Hybrid Journal   (Followers: 7)
International Journal of Materials and Product Technology     Hybrid Journal   (Followers: 4)
International Journal of Mathematical Education in Science and Technology     Hybrid Journal   (Followers: 7)
International Journal of Mathematics in Operational Research     Hybrid Journal   (Followers: 1)
International Journal of Medical Engineering and Informatics     Hybrid Journal   (Followers: 5)
International Journal of Micro Air Vehicles     Full-text available via subscription   (Followers: 4)
International Journal of Microwave and Wireless Technologies     Hybrid Journal   (Followers: 1)
International Journal of Microwave Science and Technology     Open Access   (Followers: 2)
International Journal of Mobile Network Design and Innovation     Hybrid Journal   (Followers: 3)
International Journal of Multiphase Flow     Hybrid Journal   (Followers: 2)
International Journal of Nanomanufacturing     Hybrid Journal   (Followers: 1)
International Journal of Nanoscience     Hybrid Journal   (Followers: 1)
International Journal of Nanotechnology     Hybrid Journal   (Followers: 5)
International Journal of Nanotechnology and Molecular Computation     Full-text available via subscription   (Followers: 3)
International Journal of Navigation and Observation     Open Access   (Followers: 6)
International Journal of Network Management     Hybrid Journal  
International Journal of Nonlinear Sciences and Numerical Simulation     Full-text available via subscription  
International Journal of Numerical Methods for Heat & Fluid Flow     Hybrid Journal   (Followers: 7)
International Journal of Optics     Open Access   (Followers: 1)
International Journal of Organisational Design and Engineering     Hybrid Journal   (Followers: 9)
International Journal of Pattern Recognition and Artificial Intelligence     Hybrid Journal   (Followers: 6)
International Journal of Pavement Engineering     Hybrid Journal   (Followers: 2)
International Journal of Physical Modelling in Geotechnics     Hybrid Journal   (Followers: 3)
International Journal of Plasticity     Hybrid Journal   (Followers: 6)
International Journal of Plastics Technology     Hybrid Journal  
International Journal of Polymer Analysis and Characterization     Hybrid Journal   (Followers: 5)
International Journal of Polymer Science     Open Access   (Followers: 16)
International Journal of Precision Engineering and Manufacturing     Hybrid Journal   (Followers: 5)
International Journal of Precision Engineering and Manufacturing-Green Technology     Hybrid Journal  
International Journal of Precision Technology     Hybrid Journal  
International Journal of Pressure Vessels and Piping     Hybrid Journal   (Followers: 3)
International Journal of Production Economics     Hybrid Journal   (Followers: 13)
International Journal of Quality and Innovation     Hybrid Journal   (Followers: 4)
International Journal of Quality Assurance in Engineering and Technology Education     Full-text available via subscription   (Followers: 2)
International Journal of Quality Engineering and Technology     Hybrid Journal   (Followers: 2)
International Journal of Quantum Information     Hybrid Journal  
International Journal of Rapid Manufacturing     Hybrid Journal   (Followers: 1)
International Journal of Reliability, Quality and Safety Engineering     Hybrid Journal   (Followers: 6)
International Journal of Renewable Energy Technology     Hybrid Journal   (Followers: 8)
International Journal of Robust and Nonlinear Control     Hybrid Journal   (Followers: 2)
International Journal of Science Engineering and Advance Technology     Open Access  
International Journal of Sediment Research     Full-text available via subscription   (Followers: 1)
International Journal of Self-Propagating High-Temperature Synthesis     Hybrid Journal   (Followers: 2)
International Journal of Signal and Imaging Systems Engineering     Hybrid Journal  
International Journal of Six Sigma and Competitive Advantage     Hybrid Journal  
International Journal of Social Robotics     Hybrid Journal   (Followers: 2)
International Journal of Software Engineering and Knowledge Engineering     Hybrid Journal   (Followers: 1)
International Journal of Space Science and Engineering     Hybrid Journal   (Followers: 2)
International Journal of Speech Technology     Hybrid Journal   (Followers: 4)
International Journal of Spray and Combustion Dynamics     Full-text available via subscription   (Followers: 6)
International Journal of Surface Engineering and Interdisciplinary Materials Science     Full-text available via subscription   (Followers: 1)
International Journal of Surface Science and Engineering     Hybrid Journal   (Followers: 7)
International Journal of Sustainable Engineering     Hybrid Journal   (Followers: 7)
International Journal of Sustainable Manufacturing     Hybrid Journal   (Followers: 4)
International Journal of Systems and Service-Oriented Engineering     Full-text available via subscription  
International Journal of Systems Assurance Engineering and Management     Hybrid Journal  
International Journal of Systems, Control and Communications     Hybrid Journal   (Followers: 2)
International Journal of Technoethics     Full-text available via subscription  
International Journal of Technology Management and Sustainable Development     Hybrid Journal   (Followers: 1)
International Journal of Technology Policy and Law     Hybrid Journal   (Followers: 4)
International Journal of Telemedicine and Applications     Open Access   (Followers: 2)
International Journal of Thermal Sciences     Hybrid Journal   (Followers: 7)
International Journal of Thermodynamics     Open Access   (Followers: 2)
International Journal of Turbo & Jet-Engines     Full-text available via subscription  
International Journal of Ultra Wideband Communications and Systems     Hybrid Journal  
International Journal of Vehicle Autonomous Systems     Hybrid Journal   (Followers: 1)
International Journal of Vehicle Design     Hybrid Journal   (Followers: 6)
International Journal of Vehicle Information and Communication Systems     Hybrid Journal   (Followers: 2)
International Journal of Vehicle Noise and Vibration     Hybrid Journal   (Followers: 3)
International Journal of Vehicle Safety     Hybrid Journal   (Followers: 5)
International Journal of Vehicular Technology     Open Access   (Followers: 2)
International Journal of Virtual Technology and Multimedia     Hybrid Journal   (Followers: 4)
International Journal of Wavelets, Multiresolution and Information Processing     Hybrid Journal  
International Journal on Artificial Intelligence Tools     Hybrid Journal   (Followers: 4)
International Nano Letters     Open Access   (Followers: 9)
International Review of Applied Sciences and Engineering     Full-text available via subscription  
Inverse Problems in Science and Engineering     Hybrid Journal   (Followers: 2)
Ionics     Hybrid Journal  
IPTEK The Journal for Technology and Science     Open Access  
IRBM News     Full-text available via subscription  
Irrigation and Drainage Systems     Hybrid Journal  
ISA Transactions     Full-text available via subscription   (Followers: 1)
ISRN - International Scholarly Research Notices     Open Access   (Followers: 68)
ISRN Nanotechnology     Open Access  
ISRN Signal Processing     Open Access   (Followers: 1)
ISRN Thermodynamics     Open Access  
IT Professional     Full-text available via subscription   (Followers: 3)
Journal of Biosensors & Bioelectronics     Open Access   (Followers: 2)
Journal of Advanced Manufacturing Systems     Hybrid Journal   (Followers: 5)
Journal of Aerosol Science     Hybrid Journal   (Followers: 1)
Journal of Aerospace Engineering     Full-text available via subscription   (Followers: 195)

  First | 2 3 4 5 6 7 8 9 | Last

Journal Cover   Journal of Global Optimization
  [SJR: 1.149]   [H-I: 46]   [6 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 1573-2916 - ISSN (Online) 0925-5001
   Published by Springer-Verlag Homepage  [2300 journals]
  • Second-order conditions for existence of augmented Lagrange multipliers
           for eigenvalue composite optimization problems
    • Abstract: Abstract In this paper, we mainly consider the augmented Lagrangian duality theory and explore second-order conditions for the existence of augmented Lagrange multipliers for eigenvalue composite optimization problems. In the approach, we reformulate the augmented Lagrangian introduced by Rockafellar into a new form in terms of the Moreau envelope function and characterize second-order conditions via the epi-derivatives of the augmented Lagrangian.
      PubDate: 2015-03-04
       
  • History-dependent mixed variational problems in contact mechanics
    • Abstract: We consider a new class of mixed variational problems arising in Contact Mechanics. The problems are formulated on the unbounded interval of time \([0,+\infty )\) and involve history-dependent operators. For such problems we prove existence, uniqueness and continuous dependence results. The proofs are based on results on generalized saddle point problems and various estimates, combined with a fixed point argument. Then, we apply the abstract results in the study of a mathematical model which describes the frictionless contact between a viscoplastic body and an obstacle, the so-called foundation. The process is quasistatic and the contact is modelled with normal compliance and unilateral constraint, in such a way that the stiffness coefficient depends on the history of the penetration. We prove the unique weak solvability of the contact problem, as well as the continuous dependence of its weak solution with respect to the viscoplastic constitutive function, the applied forces, the contact conditions and the initial data.
      PubDate: 2015-03-01
       
  • Branching and bounding improvements for global optimization algorithms
           with Lipschitz continuity properties
    • Abstract: Abstract We present improvements to branch and bound techniques for globally optimizing functions with Lipschitz continuity properties by developing novel bounding procedures and parallelisation strategies. The bounding procedures involve nonconvex quadratic or cubic lower bounds on the objective and use estimates of the spectrum of the Hessian or derivative tensor, respectively. As the nonconvex lower bounds are only tractable if solved over Euclidean balls, we implement them in the context of a recent branch and bound algorithm (Fowkes et al. in J Glob Optim 56:1791–1815, 2013) that uses overlapping balls. Compared to the rectangular tessellations of traditional branch and bound, overlapping ball coverings result in an increased number of subproblems that need to be solved and hence makes the need for their parallelization even more stringent and challenging. We develop parallel variants based on both data- and task-parallel paradigms, which we test on an HPC cluster on standard test problems with promising results.
      PubDate: 2015-03-01
       
  • Scalarization in set optimization with solid and nonsolid ordering cones
    • Abstract: This paper focuses on characterizations via scalarization of several kinds of minimal solutions of set-valued optimization problems, where the objective values are compared through relations between sets (set optimization). For this aim we follow an axiomatic approach based on general order representation and order preservation properties, which works in any abstract set ordered by a quasi order (i.e., reflexive and transitive) relation. Then, following this approach, we study a recent Gerstewitz scalarization mapping for set-valued optimization problems with \(K\) -proper sets and a solid ordering cone \(K\) . In particular we show a dual minimax reformulation of this scalarization. Moreover, in the setting of normed spaces ordered by non necessarily solid ordering cones, we introduce a new scalarization functional based on the so-called oriented distance. Using these scalarization mappings, we obtain necessary and sufficient optimality conditions in set optimization. Finally, whenever the ordering cone is solid, by considering suitable generalized Chebyshev norms with appropriate parameters, we show that the three scalarizations studied in the present work are coincident.
      PubDate: 2015-03-01
       
  • Conic approximation to nonconvex quadratic programming with convex
           quadratic constraints
    • Abstract: Abstract In this paper, a conic reformulation and approximation is proposed for solving a nonconvex quadratic programming problem subject to several convex quadratic constraints. The original problem is transformed into a linear conic programming problem, which can be approximated by a sequence of linear conic programming problems over the dual cone of the cone of nonnegative quadratic functions. Since the dual cone of the cone of nonnegative quadratic functions has a linear matrix inequality representation, each linear conic programming problem in the sequence can be solved efficiently using the semidefinite programming techniques. In order to speed up the convergence of the approximation sequence and relieve the computational effort in solving the linear conic programming problems, an adaptive scheme is adopted in the proposed algorithm. We prove that the lower bounds generated by the linear conic programming problems converge to the optimal value of the original problem. Several numerical examples are used to illustrate how the algorithm works and the computational results demonstrate the efficiency of the proposed algorithm.
      PubDate: 2015-03-01
       
  • Optimal clustering of a pair of irregular objects
    • Abstract: Abstract Cutting and packing problems arise in many fields of applications and theory. When dealing with irregular objects, an important subproblem is the identification of the optimal clustering of two objects. Within this paper we consider a container (rectangle, circle, convex polygon) of variable sizes and two irregular objects bounded by circular arcs and/or line segments, that can be continuously translated and rotated. In addition minimal allowable distances between objects and between each object and the frontier of a container, may be imposed. The objects should be arranged within a container such that a given objective will reach its minimal value. We consider a polynomial function as the objective, which depends on the variable parameters associated with the objects and the container. The paper presents a universal mathematical model and a solution strategy which are based on the concept of phi-functions and provide new benchmark instances of finding the containing region that has either minimal area, perimeter or homothetic coefficient of a given container, as well as finding the convex polygonal hull (or its approximation) of a pair of objects.
      PubDate: 2015-03-01
       
  • A new mathematical approach for handling DVH criteria in IMRT planning
    • Abstract: Abstract The appropriate handling of planning criteria on the cumulative dose-volume histogram (DVH) is a highly problematic issue in intensity-modulated radiation therapy (IMRT) plan optimization. The nonconvexity of DVH criteria and globality of the resulting optimization problems complicate the design of suitable optimization methods, which feature numerical efficiency, reliable convergence and optimality of the results. This work examines the mathematical structure of DVH criteria and proves the valuable properties of isotonicity/antitonicity, connectedness, invexity and sufficiency of the Karush–Kuhn–Tucker condition. These properties facilitate the use of efficient and goal-oriented optimization methods. An exemplary algorithmic realization with feasible direction methods gives rise to a functional framework for interactive IMRT planning on DVH criteria. Numerical examples on real world planning cases prove its practical capability.
      PubDate: 2015-03-01
       
  • Interactive model-based search for global optimization
    • Abstract: Abstract Single-thread algorithms for global optimization differ in the way computational effort between exploitation and exploration is allocated. This allocation ultimately determines overall performance. For example, if too little emphasis is put on exploration, the globally optimal solution may not be identified. Increasing the allocation of computational effort to exploration increases the chances of identifying a globally optimal solution but it also slows down convergence. Thus, in a single-thread implementation of model-based search exploration and exploitation are substitutes. In this paper we propose a new algorithmic design for global optimization based upon multiple interacting threads. In this design, each thread implements a model-based search in which the allocation of exploration versus exploitation effort does not vary over time. Threads interact through a simple acceptance-rejection rule preventing duplication of search efforts. We show the proposed design provides a speedup effect which is increasing in the number of threads. Thus, in the proposed algorithmic design, exploration is a complement rather than a substitute to exploitation.
      PubDate: 2015-03-01
       
  • Characterizations of efficient and weakly efficient points in nonconvex
           vector optimization
    • Abstract: Abstract In this paper, a class of nonconvex vector optimization problems with inequality constraints and a closed convex set constraint are considered. By means of Clarke derivatives and Clarke subdifferentials, a necessary and sufficient condition of weak efficiency and a sufficient criteria of efficiency are presented under suitable generalized convexity. A special case is discussed in finite dimensional space and an equivalent version of sufficient criteria of efficiency is obtained by means of Clarke derivative and linearizing cone. Some examples also are given to illustrate the main results.
      PubDate: 2015-03-01
       
  • Convergence analysis of inexact proximal point algorithms on Hadamard
           manifolds
    • Abstract: Abstract Inexact proximal point methods are extended to find singular points for multivalued vector fields on Hadamard manifolds. Convergence criteria are established under some mild conditions. In particular, in the case of proximal point algorithm, that is, \(\varepsilon _n=0\) for each \(n\) , our results improve sharply the corresponding results in Li et al. (2009). Applications to optimization problems, variational inequality problems and gradient methods are also given.
      PubDate: 2015-03-01
       
  • Constrained shortest path with uncertain transit times
    • Abstract: Abstract This paper is concerned with the constrained shortest path (CSP) problem, where in addition to the arc cost, a transit time is associated to each arc. The presence of uncertainty in transit times is a critical issue in a wide variety of world applications, such as telecommunication, traffic, and transportation. To capture this issue, we present tractable approaches for solving the CSP problem with uncertain transit times from the viewpoint of robust and stochastic optimization. To study robust CSP problem, two different uncertainty sets, \({\varGamma }\) -scenario and ellipsoidal, are considered. We show that the robust counterpart of the CSP problem under both uncertainty sets, can be efficiently solved. We further consider the CSP problem with random transit times and show that the problem can be solved by solving robust constrained shortest path problem under ellipsoidal uncertainty set. We present extensive computational results on a set of randomly generated networks. Our results demonstrate that with a reasonable extra cost, the robust optimal path preserves feasibility, in almost all scenarios under \({\varGamma }\) -scenario uncertainty set. The results also show that, in the most cases, the robust CSP problem under ellipsoidal uncertainty set is feasible.
      PubDate: 2015-02-21
       
  • A proximal point algorithm for DC fuctions on Hadamard manifolds
    • Abstract: Abstract An extension of a proximal point algorithm for difference of two convex functions is presented in the context of Riemannian manifolds of nonposite sectional curvature. If the sequence generated by our algorithm is bounded it is proved that every cluster point is a critical point of the function (not necessarily convex) under consideration, even if minimizations are performed inexactly at each iteration. Application in maximization problems with constraints, within the framework of Hadamard manifolds is presented.
      PubDate: 2015-02-20
       
  • Convex mixed integer nonlinear programming problems and an outer
           approximation algorithm
    • Abstract: Abstract In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to reformulate convex MINLP as one equivalent MILP master program. By solving a finite sequence of subproblems and relaxed MILP problems, we establish an outer approximation algorithm to find the optimal solution of this convex MINLP. The convergence of this algorithm is also presented. The work of this paper generalizes and extends the outer approximation method in the sense of dealing with convex MINLPs from differentiable case to non-differentiable one.
      PubDate: 2015-02-18
       
  • Separable cubic modeling and a trust-region strategy for unconstrained
           minimization with impact in global optimization
    • Abstract: Abstract A separable cubic model, for smooth unconstrained minimization, is proposed and evaluated. The cubic model uses some novel secant-type choices for the parameters in the cubic terms. A suitable hard-case-free trust-region strategy that takes advantage of the separable cubic modeling is also presented. For the convergence analysis of our specialized trust region strategy we present as a general framework a model \(q\) -order trust region algorithm with variable metric and we prove its convergence to \(q\) -stationary points. Some preliminary numerical examples are also presented to illustrate the tendency of the specialized trust region algorithm, when combined with our cubic modeling, to escape from local minimizers.
      PubDate: 2015-02-12
       
  • Generalized Farkas’ lemma and gap-free duality for minimax DC
           optimization with polynomials and robust quadratic optimization
    • Abstract: Abstract Motivated by robust (non-convex) quadratic optimization over convex quadratic constraints, in this paper, we examine minimax difference of convex (dc) optimization over convex polynomial inequalities. By way of generalizing the celebrated Farkas’ lemma to inequality systems involving the maximum of dc functions and convex polynomials, we show that there is no duality gap between a minimax DC polynomial program and its associated conjugate dual problem. We then obtain strong duality under a constraint qualification. Consequently, we present characterizations of robust solutions of uncertain general non-convex quadratic optimization problems with convex quadratic constraints, including uncertain trust-region problems.
      PubDate: 2015-02-12
       
  • Nonemptiness and boundedness of solution sets for vector variational
           inequalities via topological method
    • Abstract: Abstract In this paper, some characterizations of nonemptiness and boundedness of solution sets for vector variational inequalities are studied in finite and infinite dimensional spaces, respectively. By using a new proof method which is different from the one used in Huang et al. (J Optim Theory Appl 162:548–558 2014), a sufficient and necessary condition for the nonemptiness and boundedness of solution sets is established. Basing on this result, some new characterizations of nonemptiness and boundedness of solution sets for vector variational inequalities are proved. Compared with the known results in Huang et al. (2014), the key assumption that \(K_\infty \cap (F(K))^{w\circ }_C=\{0\}\) is not required in finite dimensional spaces. Furthermore, the corresponding result of Huang et al. (2014) is extended to the case of infinite dimensional spaces. Some examples are also given to illustrated the main results.
      PubDate: 2015-02-10
       
  • A homotopy method based on penalty function for nonlinear semidefinite
           programming
    • Abstract: Abstract This paper proposes a homotopy method based on a penalty function for solving nonlinear semidefinite programming problems. The penalty function is the composite function of an exponential penalty function, the eigenvalue function and a nonlinear operator mapping. Representations of its first and second order derivatives are given. Using the penalty function, a new homotopy is constructed. Global convergence of a smooth curve determined by the homotopy is proven under mild conditions. In the process of numerically tracing the curve, the method requires just the solution of a linear system of dimension \(n+2\) , whereas a homotopy method proposed by Yang and Yu (Comput Optim Appl 56(1):81–96, 2013) requires a system of dimension \(n+m(m+1)/2+1\) to be solved, where \(n\) is the number of variables while \(m\) is the order of constraint matrix. So, it is expected that the proposed method can improve the efficiency of the method proposed by Yang and Yu. Preliminary numerical experiments are presented and show that the considered algorithm is efficient for some nonlinear semidefinite programming problems.
      PubDate: 2015-02-08
       
  • Multi objective optimization of computationally expensive multi-modal
           functions with RBF surrogates and multi-rule selection
    • Abstract: Abstract GOMORS is a parallel response surface-assisted evolutionary algorithm approach to multi-objective optimization that is designed to obtain good non-dominated solutions to black box problems with relatively few objective function evaluations. GOMORS uses Radial Basic Functions to iteratively compute surrogate response surfaces as an approximation of the computationally expensive objective function. A multi objective search utilizing evolution, local search, multi method search and non-dominated sorting is done on the surrogate radial basis function surface because it is inexpensive to compute. A balance between exploration, exploitation and diversification is obtained through a novel procedure that simultaneously selects evaluation points within an algorithm iteration through different metrics including Approximate Hypervolume Improvement, Maximizing minimum domain distance, Maximizing minimum objective space distance, and surrogate-assisted local search, which can be computed in parallel. The results are compared to ParEGO (a kriging surrogate method solving many weighted single objective optimizations) and the widely used NSGA-II. The results indicate that GOMORS outperforms ParEGO and NSGA-II on problems tested. For example, on a groundwater PDE problem, GOMORS outperforms ParEGO with 100, 200 and 400 evaluations for a 6 dimensional problem, a 12 dimensional problem and a 24 dimensional problem. For a fixed number of evaluations, the differences in performance between GOMORS and ParEGO become larger as the number of dimensions increase. As the number of evaluations increase, the differences between GOMORS and ParEGO become smaller. Both surrogate-based methods are much better than NSGA-II for all cases considered.
      PubDate: 2015-02-08
       
  • A box-constrained differentiable penalty method for nonlinear
           complementarity problems
    • Abstract: Abstract In this paper, we propose a box-constrained differentiable penalty method for nonlinear complementarity problems, which not only inherits the same convergence rate as the existing \(\ell _\frac{1}{p}\) -penalty method but also overcomes its disadvantage of non-Lipschitzianness. We introduce the concept of a uniform \(\xi \) – \(P\) -function with \(\xi \in (1,2]\) , and apply it to prove that the solution of box-constrained penalized equations converges to that of the original problem at an exponential order. Instead of solving the box-constrained penalized equations directly, we solve a corresponding differentiable least squares problem by using a trust-region Gauss–Newton method. Furthermore, we establish the connection between the local solution of the least squares problem and that of the original problem under mild conditions. We carry out the numerical experiments on the test problems from MCPLIB, and show that the proposed method is efficient and robust.
      PubDate: 2015-02-05
       
  • On minimal representations by a family of sublinear functions
    • Abstract: Abstract This paper is a continuation of Grzybowski et al. (J Glob Optim 46:589–601, 2010) and is motivated by the study of exhausters i.e. families of closed convex sets. By Minkowski duality closed convex sets correspond to sublinear functions. Here we study the criteria of reducing representations of pointwise infimum of an infinite family of sublinear functions. A family \(\{f_i\}_{i\in I}\) of sublinear functions is by definition an exhaustive family of upper convex approximations of its pointwise infimum \(\inf _{i\in I}f_i\) . A family of closed convex sets is by definition an exhauster of a pointwise infimum of a family of support functions of these convex sets. We establish codependence between infimum of a subset of Minkowski–Rådström–Hörmander cone and translation property of intersection of an exhauster (Sect. 4 ), between reducing an exhauster to single convex set and shadowing property of intersection of an exhauster (Theorem 5.1) and among all four of these properties (Theorem 6.1). In Grzybowski et al. (2010) the first example of two different minimal upper exhausters of the same function was presented. Here we give an example of infinitely many minimal exhausters of the same ph-function (Example 7.2). In Sect. 8, we give a criterion of minimality of an exhauster with the help of polars of sets belonging to the exhauster. We illustrate this criterion with two interesting examples (Example 8.3).
      PubDate: 2015-02-01
       
 
 
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