Generalized scalarizing problems, called GENS and GENSLex, for obtaining Pareto optimal solutions of multicriteria optimization problems are presented in the paper. The basic properties of these scalarizing problems are described. The existence of single-criterion problems with differentiable objective functions and constraints, which are equivalent to GENS and GENSLex scalarizing problems, are...

Our aim is to provide a short analysis of the generalized variational inequality (GVI) problem from both theoretical and algorithmic point of view. First, we show connections among some well known existence theorems for GVI and for inclusions. Then, we recall the proximal point approach and a splitting algorithm for solving GVI. Finally, we propose a class of differentiable gap functions for GV...

* Correspondence: lijueyou@163. com Department of Mathematics, Chongqing Normal University, Chongqing, 400047, PR China Abstract The objective of this paper is to obtain a mixed symmetric dual model for a class of non-differentiable multiobjective nonlinear programming problems where each of the objective functions contains a pair of support functions. Weak, strong and converse duality theorems...

Any spectral function can be written as a composition function of a symmetric function f : IR 7→ IR and the eigenvalue function λ(·) : S 7→ IR, often denoted by (f ◦ λ). S is the subspace of n × n symmetric matrices. In this paper, we present some nonsmooth analysis to such spectral functions. Our main results are: (a) (f ◦ λ) is directionally differentiable if f is semidifferentiable; (b) (f ◦...

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

— The paper uses the LU-parametric representation of fuzzy numbers and fuzzy-valued functions, to obtain valid approximations of fuzzy generalized derivative and to solve fuzzy differential equations. The main result is that a fuzzy differential initial-value problem can be translated into a system of in nitely many ordinary differential equations and, by the LU-parametric representation, the i...

Adaptive Fuzzy Logic Systems trained by genetic evolution of their parameters are presented in this work. This technique is based on the aggregation of parameter perturbations. Neither the evaluation function nor the membership functions, have to be differentiable as required in most optimization techniques. In the classical Genetic Algorithms, the solution space of each parameter should be spe...

Since 1970’s B. Fuglede and others have been studying finely holomorhic functions, i.e., ‘holomorphic’ functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in [12] like a higher dimensional analogue of finely holomorphic functions.

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...