Correspondence: gaoyingimu@163. com Department of Mathematics, Chongqing Normal University, Chongqing 400047, China Abstract In this paper, a pair of nondifferentiable multiobjective fractional programming problems is formulated. For a differentiable function, we introduce the definition of higher-order (F, a, r, d)-convexity, which extends some kinds of generalized convexity, such as second or...

A PAIR OF HIGHER ORDER SYMMETRIC NONDIFFERENTIABLE MULTIOBJECTIVE MINI-MAXMIXED PROGRAMMING PROBLEMS Aruna Kumar Tripathy1 and Gayatri Devi2 1Department of Mathematics, Trident Academy of Technology, F2/A, Chandaka Industrial Estate, Bhubaneswar-24, Odisha, India, E-mail: [email protected] 2Department of Mathematics, ABIT, Cuttack, Odisha, India, E-mail: [email protected]...

* Correspondence: [email protected]. th Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand Abstract In this paper, we introduce the modified general iterative approximation methods for finding a common fixed point of nonexpansive semigroups which is a unique solution of some variational inequalities. The strong convergence theorems are established in the...

To a topological group G, we assign a naive G-spectrum DG, called the dualizing spectrum of G. When the classifying space BG is finitely dominated, we show that DG detects Poincaré duality in the sense that BG is a Poincaré duality space if and only ifDG is a homotopy finite spectrum. Secondly, we show that the dualizing spectrum behavesmultiplicatively on certain topological group extensions. ...

Considering a general optimization problem, we attach to it by means of perturbation theory two dual problems having in the constraints a subdifferential inclusion relation. When the primal problem and the perturbation function are particularized different new dual problems are obtained. In the special case of a constrained optimization problem, the classical Wolfe and Mond–Weir duals, respecti...

We consider the DC (difference of two convex functions) optimization problem ðPÞ inf x∈Xfðf 1ðxÞ− f 2ðxÞÞ þ ðg1ðAxÞ− g2ðAxÞÞg, where f 1, f 2, g1, and g2 are proper convex functions defined on locally convex Hausdorff topological vector spaces X and Y , and A is a linear continuous operator from X to Y . Adopting different tactics, two types of the Fenchel dual problems of ðPÞ are given. By usi...

The purpose of this paper is concerned with a class of multi objective programming problems in which the objective functions and constrained functions are twice differentiable and containing the support functions of a compact convex set. For such mathematic programming, to deal with its dual problem, first, the concept of second order ( , ) B p r   invexity is introduced. Further, the Mangasa...

By using properties of dualizing parametrization functions, Lagrangian functions and the epigraph technique, some sufficient and necessary conditions of the stable strong duality and strong total duality for a class of DC optimization problems are established.

We prove that among finite graph algebras and among finite flat graph algebras, dualizability, full dualizability, strong dualizability and entropicity are all equivalent. Any finite (flat) graph algebra which is not dualizable must be inherently non-κ-dualizable for every infinite cardinal κ. A new, general method for proving strong duality is presented.

To minimize the primal support vector machine (SVM) problem, we propose to use iterative majorization. To do so, we propose to use iterative majorization. To allow for nonlinearity of the predictors, we use (non)monotone spline transformations. An advantage over the usual kernel approach in the dual problem is that the variables can be easily interpreted. We illustrate this with an example from...