We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. Sufficient optimality conditions are presented by using generalized convexity and certain regularity conditions. We formulate Wolfe-type dual and Mond-Weirtype dual problems for our nonsmo...

In the first part of this talk (two weeks ago), I sketched my work on the lattice theory of the weak order. The key point was that the lattice structure provides an alternate algebraic structure on a finite Coxeter group. One interesting aspect of this alternate structure is the study of quotients of the weak order modulo lattice congruences. The talk will start with a very brief recap of the r...

In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficien...

11 A classical theorem by Ritt states that all the complete decomposition chains of a univariate polynomial satisfying a certain tameness condition have the same length. In this paper we present 13 our conclusions about the generalization of these theorem in the case of finite coefficient fields when the tameness condition is dropped. 15 © 2005 Published by Elsevier Inc.

We present some fixed point results for mappings which satisfy Hardy–Rogers rational type, quasicontraction type, weak contraction type and generalized fψ type cyclic conditions in 0-complete partial metric spaces. Presented results generalize or improve many existing fixed point theorems in the literature. To demonstrate our results, we give throughout the paper some examples. One of the possi...

In this paper we introduce a broad class of nonlinear mappings which contains the class of contractive mappings and the class of generalized hybrid mappings in a Hilbert space. Then we prove an attractive point theorem for such mappings in a Hilbert space. Furthermore, we prove a mean convergence theorem of Baillon’s type without convexity in a Hilbert space. Finally, we prove a weak convergenc...

The aim of the present paper is to obtain a number of Kuhn-Tucker type sufficient optimality conditions for a feasible solution to be an efficient solution under the assumptions of the new notions of weak strictly pseudo quasi α-univex, strong pseudo quasi α-univex, and weak strictly pseudo α-univex vector valued functions. We also derive the duality theorems for Mond-Weir and general Mond-Wei...

In this paper, we introduce two types of the Levitin-Polyak well-posedness for the system of weak generalized vector equilibrium problems. By using the gap function of the system of weak generalized vector equilibrium problems, we establish the equivalent relationship between the two types of Levitin-Polyak well-posedness of the system of weak generalized vector equilibrium problems and the cor...