Optimality and duality for generalized fractional programming involving nonsmooth (F, ρ)-convex functions

AbstractUsing a parametric approach, we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing (F, ρ)-convex function

Nonsmooth multiobjective fractional programming with generalized convexity

En el artículo estudiamos una clase de problemas fraccionales multiobjetivos no convexos y no diferenciables. Usamos la transformación propuesta por Dinkelbach [2] y Jagannathan [4] y obtenemos condiciones de optimalidad para soluciones débilmente eficientes de dichos problemas. Además, definimos un problema dual y establecemos algunos resultados sobre dualidad. Para lograrlo, utilizamos una noción de convexidad generalizada llamada KT-invexidad. El artículo generaliza los resultados obtenidos por Osuna-Gómez et al. en [6], en donde los autores consideran problemasIn this paper we study a class of nonconvex and nondifferentiable multiobjective fractional problems. We use the transformation proposed by Dinkelbach [2] and Jagannathan [4] and we obtain optimality conditions for weakly efficient solutions for these problems. Furthermore, we define a dual problem and we establish some results on duality. To obtain our results, we use a notion of generalized convexity, called KT-invexity. Our paper generalizes the results given by Osuna-Gómez et al. in [6], where the authors considered smooth problems.    &nbsp

Necessary Optimality Conditions for Continuous-Time Optimization Problems with Equality and Inequality Constraints

The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit function theorem are used in order to establish such necessary conditions.Comment: 20 page

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

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Duality without constraint qualification in nonsmooth optimization

We are concerned with a nonsmooth multiobjective optimization problem with inequality constraints. In order to obtain our main results, we give the definitions of the generalized convex functions based on the generalized directional derivative. Under the above generalized convexity assumptions, sufficient and necessary conditions for optimality are given without the need of a constraint qualification. Then we formulate the dual problem corresponding to the primal problem, and some duality results are obtained without a constraint qualification

Generalized Fractional Programming With User Interaction

The present paper proposes a new approach to solve generalized fractional programming problems through user interaction. Capitalizing on two alternatives, we review the Dinkelbach-type methods and set forth the main difficulty in applying these methods. In order to cope with this difficulty, we propose an approximation approach that can be controlled by a predetermined parameter. The proposed approach is promising particularly when a decision maker is involved in the solution process and agrees upon finding an effective but nearoptimal value in an efficient manner. The decision maker is asked to decide the parameter and our analysis shows how good is the value found by the approximation corresponding to this parameter. In addition, we present several observations that may be suitable for boosting up the performance of the proposed approach. Finally, we support our discussion through extensive numerical experiments