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11th International Conference on Computational Science and Its Applications (ICCSA)

作者： Pereira, Ana I. Fernandes, Edite M. G. P. Polytech Inst Braganca ESTiG Gab 54 P-5301857 Braganca Portugal Univ Minho Algoritmi R&D Ctr P-4710057 Braga Portugal

ISBN: (纸本)9783642219306;9783642219313

semi-infinite programming (SIP) problems can be efficiently solved by reduction type methods. Here, we present a new reduction method for SIP, where the multi-local optimization is carried out with a multi-local branch-and-bound method, the reduced (finite) problem is approximately solved by an interior point method, and the global convergence is promoted through a two-dimensional filter line search. Numerical experiments with a set of well-known problems are shown.

关键词： Nonlinear Optimization semi-infinite programming Global Optimization

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Sufficient and Necessary Conditions of Optimal Solutions of semi-infinite Convex Programing

Sufficient and Necessary Conditions of Optimal Solutions of ...

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IEEE International Conference on Grey Systems and Intelligent Services (GSIS)

作者： Zhang, Changwen Univ Jinan Sch Math Sci Jinan 250022 Shandong Peoples R China

This paper investigates characterizations of semi-infinite convex programming, and obtains conditions of optimal solutions of semi-infinite convex programming by using saddle point criteria.

ISBN: (纸本)9781509066681

This paper investigates characterizations of semi-infinite convex programming, and obtains conditions of optimal solutions of semi-infinite convex programming by using saddle point criteria.

关键词： semi-infinite programming saddle point criteria support function support hyerplane epigraph

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Necessary conditions for nonsmooth multiobjective semi-infinite problems using Michel-Penot subdifferential

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DECISIONS IN ECONOMICS AND FINANCE 2017年第1-2期40卷 103-113页

作者： Caristi, Giuseppe Ferrara, Massimiliano Univ Messina Dept Econ Via Verdi75 Messina Italy Univ Reggio Calabria Dept Law & Econ Reggio Di Calabria Italy

In this paper, for a nonsmooth multiobjective semi-infinite optimization problem, where the objective and constraint functions are locally Lipschitz, some constraint qualifications are given, and Kuhn-Tucker-type nece... 详细信息

关键词： semi-infinite programming Multiobjective optimization Constraint qualification Optimality conditions Michel-Penot subdifferential

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A Norm-Relaxed SQP Method of Strongly Sub-Feasible Direction for Finely Discretized Problems from semi-infinite programming

A Norm-Relaxed SQP Method of Strongly Sub-Feasible Direction...

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2011 IEEE International Conference on Computer Science and Automation Engineering(CSAE 2011)

作者： Qingjuan Xu Department of Mathematics Shanghai University Shanghai,China Jinbao Jian College of Mathematics and Information Guangxi University Nanning,China Daolan Han College of Mathematics and Computer Science Guangxi University for Nationalities Nanning,China

In this paper,we discuss a kind of finely discretized problem from semi-infinite *** the idea of the norm-relaxed SQP method of strongly sub-feasible direction method with the technique of updating discretization index set,we present a new algorithm with arbitrary initial point for the discussed *** each iteration,an improved direction is obtained by solving only one direction finding subproblem,and some appropriate constraints are chosen to reduce the computational *** mild assumptions such as Mangasarian-Fromovitz Constraint Qualification(MFCQ),the proposed algorithm possesses weak global ***,some primary numerical experiments are reported.

关键词： semi-infinite programming discretized problem norm-relaxed SQP method strongly sub-feasible direction method global convergence.

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Modeling probability densities with sums of exponentials via polynomial approximation

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2016年 292卷 513-525页

作者： Dumitrescu, Bogdan Sicleru, Bogdan C. Avram, Florin Univ Politehn Bucuresti Dept Automat Control & Comp Bucharest 060042 Romania Tampere Univ Technol Dept Signal Proc FIN-33101 Tampere Finland Univ Pau & Pays Adour F-64010 Pau France

We propose a method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on shape-constrained optimization with exponential functions. Each function is lower and upper bounded on sub-intervals by low-degree polynomials. Thus, the constraints can be approximated with polynomial inequalities that can be implemented with linear matrix inequalities. Convexity is preserved, but the problem has now a finite number of constraints. We show how to take advantage of the properties of the exponential function in order to build quickly accurate approximations. The problem used for illustration is the least-squares fitting of a positive sum of exponentials to an empirical probability density function. When the exponents are given, the problem is convex, but we also give a procedure for optimizing the exponents. Several examples show that the method is flexible, accurate and gives better results than other methods for the investigated problems. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Optimization Density fitting semi-infinite programming Sum of exponentials Polynomial approximation

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Data-driven chance constrained stochastic program

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MATHEMATICAL programming 2016年第1-2期158卷 291-327页

作者： Jiang, Ruiwei Guan, Yongpei Univ Arizona Dept Syst & Ind Engn Tucson AZ 85721 USA Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

In this paper, we study data-driven chance constrained stochastic programs, or more specifically, stochastic programs with distributionally robust chance constraints (DCCs) in a data-driven setting to provide robust solutions for the classical chance constrained stochastic program facing ambiguous probability distributions of random parameters. We consider a family of density-based confidence sets based on a general -divergence measure, and formulate DCC from the perspective of robust feasibility by allowing the ambiguous distribution to run adversely within its confidence set. We derive an equivalent reformulation for DCC and show that it is equivalent to a classical chance constraint with a perturbed risk level. We also show how to evaluate the perturbed risk level by using a bisection line search algorithm for general -divergence measures. In several special cases, our results can be strengthened such that we can derive closed-form expressions for the perturbed risk levels. In addition, we show that the conservatism of DCC vanishes as the size of historical data goes to infinity. Furthermore, we analyze the relationship between the conservatism of DCC and the size of historical data, which can help indicate the value of data. Finally, we conduct extensive computational experiments to test the performance of the proposed DCC model and compare various -divergence measures based on a capacitated lot-sizing problem with a quality-of-service requirement.

关键词： Stochastic programming Chance constraints semi-infinite programming

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Characterizing optimal wages in principal- agent problems without using the first- order approach

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OPTIMIZATION 2016年第2期65卷 467-478页

作者： Nasri, Mostafa McGill Univ Dept Mech Engn Montreal PQ Canada

The analysis of the principal-agent problem usually requires the classical first-order approach (FOA). However, the validity of the FOA makes restrictive assumptions on the problem under consideration such as the convexity of the distribution function condition. The main aim of this paper is to compute the optimal wages and characterize a closed form solution to the risk-neutral principal-agent problem with limited liability constraints. The development in this paper mainly invokes certain techniques in the semi-infinite programming rather than the FOA.

关键词： convexity of the distribution function condition duality first-order approach monotone likelihood ratio principal-agent problem semi-infinite programming

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Optimality Conditions for semi-infinite and Generalized semi-infinite Programs Via Lower Order Exact Penalty Functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2016年第3期169卷 984-1012页

作者： Yang, Xiaoqi Chen, Zhangyou Zhou, Jinchuan Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China South West Jiao Tong Univ Coll Math & Stat Chengdu Peoples R China Shandong Univ Technol Sch Sci Dept Math Zibo Peoples R China

In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs by employing lower order exact penalty functions and the condition that the generalized second-order directional derivative of the constraint function at the candidate point along any feasible direction for the linearized constraint set is non-positive. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty functions. We employ lower order integral exact penalty functions and the second-order generalized derivative of the constraint function to establish optimality conditions for semi-infinite programs. We adopt the exact penalty function technique in terms of a classical augmented Lagrangian function for the lower-level problems of generalized semi-infinite programs to transform them into standard semi-infinite programs and then apply our results for semi-infinite programs to derive the optimality condition for generalized semi-infinite programs. We will give various examples to illustrate our results and assumptions.

关键词： semi-infinite programming Generalized semi-infinite program Optimality conditions Lower-order exact penalization Generalized second-order derivative

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Slater CQ, optimality and duality for quasiconvex semi-infinite optimization problems

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2016年第1期434卷 638-651页

作者： Kanzi, Nader Soleimani-damaneh, Majid PNU Dept Math Tehran Iran Univ Tehran Coll Sci Sch Math Stat & Comp Sci Tehran Iran Inst Res Fundamental Sci IPM Sch Math Tehran Iran

In this paper, we introduce and study the Slater constraint qualification (CQ) for a semi-infinite optimization problem with upper-semicontinuous quasiconvex objective and constraint functions. Then, some Karush-Kuhn-Tucker (KKT) type necessary and sufficient optimality conditions as well as duality results are derived. The final part of the paper is devoted to a linear characterization of optimality and the gap function for considered semi-infinite problem. (C) 2015 Elsevier Inc. All rights reserved.

关键词： semi-infinite programming Quasiconvex function Slater constraint qualification Optimality conditions

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Feasible Method for Generalized semi-infinite programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2010年第2期146卷 419-443页

作者： Stein, O. Winterfeld, A. Karlsruhe Inst Technol Inst Operat Res Karlsruhe Germany Fraunhofer Inst Techno & Wirtschaftsmath Kaiserslautern Germany

In this paper, we analyze the outer approximation property of the algorithm for generalized semi-infinite programming from Stein and Still (SIAM J. Control Optim. 42:769-788, 2003). A simple bound on the regularization error is found and used to formulate a feasible numerical method for generalized semi-infinite programming with convex lower-level problems. That is, all iterates of the numerical method are feasible points of the original optimization problem. The new method has the same computational cost as the original algorithm from Stein and Still (SIAM J. Control Optim. 42:769-788, 2003). We also discuss the merits of this approach for the adaptive convexification algorithm, a feasible point method for standard semi-infinite programming from Floudas and Stein (SIAM J. Optim. 18:1187-1208, 2007).

关键词： semi-infinite programming Interior-point method Mathematical program with equilibrium constraints Bilevel programming Design centering

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