Sufficient optimality criteria and duality for multiobjective variational control problems with G-type I objective and constraint functions

In the paper, we introduce the concepts of G-type I and generalized G-type I functions for a new class of nonconvex multiobjective variational control problems. For such nonconvex vector optimization problems, we prove sufficient optimality conditions for weakly efficiency, efficiency and properly efficiency under assumptions that the functions constituting them are G-type I and/or generalized G-type I objective and constraint functions. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem is given and several duality results are established under (generalized) G-type I objective and constraint functions

Proper efficiency and duality for a new class of nonconvex multitime multiobjective variational problems

In this paper, a new class of generalized of nonconvex multitime multiobjective variational problems is considered. We prove the sufficient optimality conditions for efficiency and proper efficiency in the considered multitime multiobjective variational problems with univex functionals. Further, for such vector variational problems, various duality results in the sense of Mond-Weir and in the sense of Wolfe are established under univexity. The results established in the paper extend and generalize results existing in the literature for such vector variational problems

Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization

This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraint

The proximal point method for locally lipschitz functions in multiobjective optimization with application to the compromise problem

This paper studies the constrained multiobjective optimization problem of finding Pareto critical points of vector-valued functions. The proximal point method considered by Bonnel, Iusem, and Svaiter [SIAM J. Optim., 15 (2005), pp. 953–970] is extended to locally Lipschitz functions in the finite dimensional multiobjective setting. To this end, a new (scalarization-free) approach for convergence analysis of the method is proposed where the first-order optimality condition of the scalarized problem is replaced by a necessary condition for weak Pareto points of a multiobjective problem. As a consequence, this has allowed us to consider the method without any assumption of convexity over the constraint sets that determine the vectorial improvement steps. This is very important for applications; for example, to extend to a dynamic setting the famous compromise problem in management sciences and game theory.Fundação de Amparo à Pesquisa do Estado de GoiásConselho Nacional de Desenvolvimento Científico e TecnológicoCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorMinisterio de Economía y CompetitividadAgence nationale de la recherch

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

[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

Nonconvex optimization for pricing and hedging in imperfect markets.

The paper deals with imperfect financial markets and provides new methods to overcome many inefficiencies caused by frictions. Transaction costs are quite general and far from linear or convexo The concepts of pseudoarbitrage and efficiency are introduced and deeply analyzed by means of both scalar and vector optimization problems. Their optimality conditions and solutions yield strategies to invest and hedging portfolios, as well as bid-ask spread improvements. They also point out the role of coalitions when dealing with these markets. Several sensitivity results will permit us to show that a significant transaction costs reduction is very often feasible in practice, as well as to measure its effect on the general efficiency of the market. AII these findings may be especially important for many emerging and still illiquid spot or derivative markets (electricity markets, com odity markets, markets related to weather, infiation-linked or insurance-linked derivatives, etc.).Global optimization; Pseudoarbitrage; Spread reduction; Balance point;

Tangential Extremal Principles for Finite and Infinite Systems of Sets, I: Basic Theory

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. The first part of the paper concerns the basic theory of tangential extremal principles while the second part presents applications to problems of semi-infinite programming and multiobjective optimization

Multiobjective optimal power flow using a semidefinite programming-based model

In spite of the significant advance achieved in the development of optimal power flow (OPF) programs, most of the solution methods reported in the literature have considerable difficulties in dealing with different-nature objective functions simultaneously. By leveraging recent progress on the semidefinite programming (SDP) relaxations of OPF, in the present article, attention is focused on modeling a new SDP-based multiobjective OPF (MO-OPF) problem. The proposed OPF model incorporates the classical ϵ-constraint approach through a parameterization strategy to handle the multiple objective functions and produce Pareto front. This article emphasizes the extension of the SDP-based model for MO-OPF problems to generate globally nondominated Pareto optimal solutions with uniform distribution. Numerical results on IEEE 30-, 57-, 118-bus, and Indian utility 62-bus test systems with all security and operating constraints show that the proposed convex model can produce the nondominated solutions with no duality gap in polynomial time, generate efficient Pareto set, and outperform the well-known heuristic methods generally used for the solution of MO-OPF. For instance, in comparison with the obtained results of NSGA-II for the 57-bus test system, the best compromise solution obtained by SDP has 1.55% and 7.42% less fuel cost and transmission losses, respectively.©2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.fi=vertaisarvioitu|en=peerReviewed

Optimality and duality for a class of nonsmooth fractional multiobjective optimization problems (Nonlinear Analysis and Convex Analysis)

In this paper, we establish necessary optimality conditions for (weakly) efficient solutions of a nonsmooth fractional multiobjective optimization problem with inequality and equality constraints by employing some advanced tools of variational analysis and generalized differentiation. Sufficient optimality conditions for such solutions to the considered problem are also provided by means of introducing (strictly) convex-affine functions. Along with optimality conditions, we formulate a dual problem to the primal one and explore weak, strong and converse duality relations between them under assumptions of (strictly) convex-affine functions