[01] Savin Treanţă, Faculty of Applied Sciences, University Politehnica of Bucharest, Bucharest, Romania. [02] Elena-Laura Dudaş, Faculty of Applied Sciences, University Politehnica of Bucharest, Bucharest, Romania.

The main goal of this paper is to formulate and prove necessary and sufficient conditions of efficiency for a class of matrix variational problems (MVP). Under (ρ,b)-quasiinvexity assumptions, we establish sufficient efficiency conditions for a feasible solution in (MVP). The method of investigation used in this work is based on employing of several adequate variational calculus techniques in the study of some vector variational problems. Our results extend, unify and improve several theorems in the current literature.

(Normal) Efficient Solution, (ρ,b)-Quasiinvexity, Matrix Variational Problem

[01] F. A. Valentine, The problem of Lagrange with differentiable inequality as added side conditions, Contributions to the Calculus of Variations, Univ. of Chicago Press, pp. 407-448, 1937. [02] St. Mititelu, Efficiency conditions for multiobjective fractional variational problems, Appl. Sciences (APPS) 10, pp. 162-175, 2008. [03] S. Treanta, On a vector optimization problem involving higher order derivatives, U. P. B. Scientific Bulletin, Series A, 77, 1, pp. 115-128, 2015. [04] S. Treanta, Multiobjective fractional variational problem on higher-order jet bundles, Commun. Math. Stat., 4, 3, pp. 323-340, 2016. [05] M. A. Geoffrion, Proper efficiency and the theory of vector minimization, J. Math. Anal. Appl., 149, 6, pp. 618-630, 1968. [06] V. Preda, On Mond-Weir duality for variational problems, Rev. Roumanie Math. Pures Appl., 28, 2, pp. 155-164, 1993. [07] S. Treanta, C. Udriste, On Efficiency Conditions for Multiobjective Variational Problems Involving Higher Order Derivatives, Proceedings of the 15th International Conference on Automatic Control, Modelling & Simulation (ACMOS’13), Brasov, Romania, June 1-3, pp. 157-164, 2013. [08] V. Chankong, Y. Y. Haimes, Multiobjective decisions making: theory and methodology, North Holland, New York, 1983. [09] A. Chinchuluun, P. M. Pardalos, A survey of recent developments in multiobjective optimization, Ann. Oper. Res., 154, 1, pp. 29-50, 2007. [10] R. Jagannathan, Duality for nonlinear fractional programming, Z. Oper. Res., 17, pp. 1-3, 1973.