in this paper, convex semi-infinite programming is converted to an optimal control model of neural networks and the optimal control model is solved by iterative dynamic programming method. in final, numerical examples are provided for illustration of the purposed method.

Using the concept of majorant sequences (see [4, ch. XXI], [5], [7], [8]) some new inequalities for Walsh polynomials with complex semi-monotone, complex semi-convex, complex monotone and complex convex coefficients are given.

We characterize generalized extreme points of compact convex sets. In particular, we show that if the polyconvex hull is convex in m×n , min(m,n) 6 2, then it is constructed from polyconvex extreme points via sequential lamination. Further, we give theorems ensuring equality of the quasiconvex (polyconvex) and the rank-1 convex envelopes of a lower semicontinuous function without explicit conve...

We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: −A x 3 t ∈ N K t, ẋ t ; A ẍ t F t, x t , ẋ t , ẍ t G x t , ẋ t , ẍ t a.e. 0, T , A ẍ t ∈ K t, ẋ t , a.e. t ∈ 0, T , x 0 x0, ẋ 0 u0, ẍ 0 υ0, where T > 0, K is a nonconvex Lipschitz set-valued mapping, F is an unbounded scalarly upper semicontinuous convex set-v...

In this paper, we show that a closed convex set C of a Banach space is strongly proximinal (proximinal, resp.) in every Banach space isometrically containing it if and only if C is locally (weakly, resp.) compact. As a consequence, it is proved that local compactness of C is also equivalent to that for every Banach space Y isometrically containing it, the metric projection from Y to C is nonemp...

In this paper, we give twoweak conditions for a lower semi-continuous function on the n-dimensional Euclidean space Rn to be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions.

Given x0, a point of a convex subset C of an Euclidean space, the two following statements are proven to be equivalent: (i) any convex function f : C → R is upper semi-continuous at x0, and (ii) C is polyhedral at x0. In the particular setting of closed convex mappings and Fσ domains, we prove that any closed convex function f : C → R is continuous at x0 if and only if C is polyhedral at x0. Th...

A concept of synchronicity associated with convex functions in linear spaces and a μ Cebyšev type inequality are given. Applications for norms, semi-inner products and for convex functions of several real variables are also given.

We study regularity properties of the subdifferential of proper lower semicontinuous convex functions in Hilbert spaces. More precisely, we investigate the metric regularity and subregularity, the strong regularity and subregularity of such a subdifferential. We characterize each of these properties in terms of a growth condition involving the function.

In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach.