363 research outputs found

    Nondifferentiable G-Mond-Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions

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    [EN] In this article, a pair of nondifferentiable second-order symmetric fractional primal-dual model (G-Mond-Weir type model) in vector optimization problem is formulated over arbitrary cones. In addition, we construct a nontrivial numerical example, which helps to understand the existence of such type of functions. Finally, we prove weak, strong and converse duality theorems under aforesaid assumptions.Dubey, R.; Mishra, LN.; SĂĄnchez Ruiz, LM. (2019). Nondifferentiable G-Mond-Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions. Symmetry (Basel). 11(11):1-18. https://doi.org/10.3390/sym11111348S118111

    Second-order symmetric duality with cone constraints

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    AbstractWolfe and Mond–Weir type second-order symmetric duals are formulated and appropriate duality theorems are established under η-bonvexity/η-pseudobonvexity assumptions. This formulation removes several omissions in an earlier second-order primal dual pair introduced by Devi [Symmetric duality for nonlinear programming problems involving η-bonvex functions, European J. Oper. Res. 104 (1998) 615–621]

    Set optimization - a rather short introduction

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    Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

    Nondifferentiable multiobjective programming problem under strongly K-Gf-pseudoinvexity assumptions

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    [EN] In this paper we consider the introduction of the concept of (strongly) K-G(f)-pseudoinvex functions which enable to study a pair of nondifferentiable K-G- Mond-Weir type symmetric multiobjective programming model under such assumptions.Dubey, R.; Mishra, LN.; Sánchez Ruiz, LM.; Sarwe, DU. (2020). Nondifferentiable multiobjective programming problem under strongly K-Gf-pseudoinvexity assumptions. Mathematics. 8(5):1-11. https://doi.org/10.3390/math8050738S11185Antczak, T. (2007). New optimality conditions and duality results of type in differentiable mathematical programming. Nonlinear Analysis: Theory, Methods & Applications, 66(7), 1617-1632. doi:10.1016/j.na.2006.02.013Antczak, T. (2008). On G-invex multiobjective programming. Part I. Optimality. Journal of Global Optimization, 43(1), 97-109. doi:10.1007/s10898-008-9299-5Ferrara, M., & Viorica-Stefanescu, M. (2008). Optimality conditions and duality in multiobjective programming with invexity. YUJOR, 18(2), 153-165. doi:10.2298/yjor0802153fChen, X. (2004). Higher-order symmetric duality in nondifferentiable multiobjective programming problems. Journal of Mathematical Analysis and Applications, 290(2), 423-435. doi:10.1016/j.jmaa.2003.10.004Long, X. (2013). Sufficiency and duality for nonsmooth multiobjective programming problems involving generalized univex functions. Journal of Systems Science and Complexity, 26(6), 1002-1018. doi:10.1007/s11424-013-1089-6Dubey, R., Mishra, L. N., & Sánchez Ruiz, L. M. (2019). Nondifferentiable G-Mond–Weir Type Multiobjective Symmetric Fractional Problem and Their Duality Theorems under Generalized Assumptions. Symmetry, 11(11), 1348. doi:10.3390/sym11111348Pitea, A., & Postolache, M. (2011). Duality theorems for a new class of multitime multiobjective variational problems. Journal of Global Optimization, 54(1), 47-58. doi:10.1007/s10898-011-9740-zPitea, A., & Antczak, T. (2014). Proper efficiency and duality for a new class of nonconvex multitime multiobjective variational problems. Journal of Inequalities and Applications, 2014(1). doi:10.1186/1029-242x-2014-333Dubey, R., Deepmala, & Narayan Mishra, V. (2020). Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints. Statistics, Optimization & Information Computing, 8(1), 187-205. doi:10.19139/soic-2310-5070-60

    Higher Order Duality for Vector Optimization Problem over Cones Involving Support Functions

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    In this paper, we consider a vector optimization problem over cones involving support functions in  objective as well as constraints and associate a unified higher order dual to it.  Duality result have been established under the conditions of higher order cone convex and related functions.  A number of previously studied problems appear as special cases. Keywords: Vector optimization, Cones, Support Functions, Higher Order Duality

    Domination and Decomposition in Multiobjective Programming

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    During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

    Higher order duality in multiobjective fractional programming with support functions

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    AbstractIn this paper a new class of higher order (F,ρ,σ)-type I functions for a multiobjective programming problem is introduced, which subsumes several known studied classes. Higher order Mond–Weir and Schaible type dual programs are formulated for a nondifferentiable multiobjective fractional programming problem where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are studied in both the cases assuming the involved functions to be higher order (F,ρ,σ)-type I. A number of previously studied problems appear as special cases
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