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Stable and Total Fenchel Duality for Composed Convex Optimization Problems

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Acta Mathematicae Applicatae Sinica 2018年第4期34卷 813-827页

作者： Dong-hui FANG Xian-yun WANG College of Mathematics and Statistics Jishou University

In this paper, we consider the composed convex optimization problem which consists in minimizing the sum of a convex function and a convex composite function. By using the properties of the epigraph of the conjugate functions and the subdifferentials of convex functions, we give some new constraint qualifications which completely characterize the strong Fenchel duality and the total Fenchel duality for composed convex optimiztion problem in real locally convex Hausdorff topological vector spaces.

关键词： Composed convex optimization problem constraint qualifications strong duality total duality

Sufficiency and Duality for Nonsmooth Interval-Valued Optimization Problems via Generalized Invex-Infine Functions

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Journal of the Operations Research Society of China 2023年第3期11卷 505-527页

作者： Izhar Ahmad Krishna Kummari S.Al-Homidan Department of Mathematics and Statistics King Fahd University of Petroleum and MineralsDhahran31261Saudi Arabia Department of Mathematics School of ScienceGITAMHyderabad CampusHyderabad502329India

In this paper,a new concept of generalized-affineness type of functions is *** class of functions is more general than some of the corresponding ones discussed in Chuong(Nonlinear Anal Theory Methods Appl 75:5044–5052,2018),Sach et al.(J Global Optim 27:51–81,2003)and Nobakhtian(Comput Math Appl 51:1385–1394,2006).These concepts are used to discuss the sufficient optimality conditions for the interval-valued programming problem in terms of the limiting/Mordukhovich subdifferential of locally Lipschitz ***,two types of dual problems,namely Mond–Weir type and mixed type duals are formulated for an interval-valued programming problem and usual duality theorems are *** results improve and generalize the results appeared in Kummari and Ahmad(UPB Sci Bull Ser A 82(1):45–54,2020).

关键词： Mordukhovich subdifferential Locally Lipschitz functions Generalized invex-infine function Interval-valued programming LU-optimal constraint qualifications Duality

Necessary Optimality Conditions for a Class of Nonsmooth Vector Optimization

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Acta Mathematicae Applicatae Sinica 2009年第1期25卷 87-94页

作者： Hui-xian Wu He-zhi Luo College of Science Hangzhou Dianzi University Hangzhou 310018 China Department of Applied Mathematics Zhejiang University of Technology Hangzhou 310032 China

The Kuhn-Tucker type necessary conditions of weak efficiency are given for the problem of mini- mizing a vector function whose each component is the sum of a differentiable function and a convex function, subjcct to a set of differentiable nonlinear inequalities on a convex subset C of R^n, under the conditions similar to the Abadie constraint qualification, or the Kuhn-Tucker constraint qualification, or the Arrow-Hurwicz-Uzawa constraint qualification.

关键词： Vector optimization problems necessary conditions weak efficiency constraint qualifications

KUHN-TUCKER NECESSARY CONDITIONS FOR (h, ψ)-MULTIOBJECTIVE OPTIMIZATION PROBLEMS

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Journal of Systems Science & Complexity 2004年第4期17卷 472-484页

作者： XUYihong LIUSanyang DepartmentofMathematics NanchangUniversityNanchang330047 DepartmentofAppliedMathematics XidianUniversityXi'an710071China

Five kinds of cones are introduced, which are used to establish the constraints qualifications, under which the generalized Kuhn-Tucker necessary conditions are developed for a class of generalized (h,φ)-differentiable single-objective and multiobjective programming problems by using Motzkin's alternative theorem and Ben-Tal generalized algebraic operations.

关键词： cones (h,φ)-differentiable functions kuhn-tucker necessary conditions constraint qualifications optimal solutions efficient solutions

Guignard’s constraint Qualification (GCQ) and Multiobjective Optimisation Problems

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Journal of Applied Mathematics and Physics 2022年第7期10卷 2356-2367页

作者： H. S. Faruque Alam Ganesh Chandra Ray Department of Mathematics University of Chittagong Chattogram Bangladesh

Investigation of optimality conditions has been one of the most interesting topics in the theory of multiobjective optimisation problems (MOP). To derive necessary optimality conditions of MOP, we consider assumptions called constraints qualifications. It is recognised that Guignard constraint Qualification (GCQ) is the most efficient and general assumption for scalar objective optimisation problems;however, GCQ does not ensure Karush-Kuhn Tucker (KKT) necessary conditions for multiobjective optimisation problems. In this paper, we investigate the reasons behind that GCQ are not allowed to derive KKT conditions in multiobjective optimisation problems. Furthermore, we propose additional assumptions that allow one to use GCQ to derive necessary conditions for multiobjective optimisation problems. Finally, we also include sufficient conditions for multiobjective optimisation problems.

关键词： constraint qualifications Multiobjective Optimization Karush Kuhn-Tucker Conditions constraint Optimization