We consider the generalized minimax programming problem (P) in which functions are locally Lipschitz (G, β)-invex. Not only G-sufficient but also G-necessary optimality conditions are established for problem (P). With G-necessary optimality conditions and (G, β)-invexity on hand, we construct dual problem (DI) for the primal one (P) and prove duality results between problems (P) and (DI). These...

The aim of this paper is to study first order optimality conditions for ideal efficient points in the Löwner partial order, when the data functions of the minimization problem are differentiable and convex with respect to the cone of symmetric semidefinite matrices. We develop two sets of first order necessary and sufficient conditions. The first one, formally very similar to the classical Karu...

In this paper, we study the asymptotic behaviour of a parabolic optimal control problem in a domain Ωε ⊂ Rn , whose boundary ∂Ωε contains a highly oscillating part. We consider this problem with two different classes of Dirichlet boundary controls, and, as a result, we provide its asymptotic analysis with respect to the different topologies of homogenization. It is shown that the mathematical d...

Existence and stability of travelling waves are conveniently studied on unbounded domains , for instance, on the real line. Motivated by numerical and experimental studies, we investigate the eeects of truncating the unbounded domain to a large but bounded domain. It is shown that periodic boundary conditions accurately reproduce the L 2-spectrum of the unbounded domain, whereas separated bound...

L denotes the classical curve length, s is the arc-length parameter, and Γ : [0, L]→ Ω is a curve with non-vanishing velocity vector. κ is the curvature and α , β are two positively weighted functions computed by the optimally oriented flux filter [2]. Our first step is to cast the elastica energy (5) in the form of path length with respect to a degenerate Finsler metric. For that purpose, let ...

In this paper, we study second-order necessary optimality conditions for a discrete optimal control problem with nonconvex cost functions and state-control constraints. By establishing an abstract result on second-order necessary optimality conditions for a mathematical programming problem, we derive second-order necessary optimality conditions for a discrete optimal control problem.

optimization of cutting conditions is a non-linear optimization with constraint and it is very important to the increase of productivity and the reduction of costs. in recent years, several evolutionary and meta-heuristic optimization algorithms were introduced. the cuckoo optimization algorithm (coa) is one of several recent and powerful meta-heuristics which is inspired by the cuckoos and the...

Error bounds for cone inclusion problems in Banach spaces are established under conditions weaker than Robinson’s constraint qualification. The results allow the cone to be more general than the origin and therefore also generalize a classical error bound result concerning equality-constrained sets in optimization. Applications in finite-dimensional differentiable inequalities and in tangent co...

We provide necessary optimality conditions for a general class of discounted infinitehorizon dynamic optimization problems. As part of the resulting maximum principle we obtain explicit bounds on the adjoint variable, stronger than the transversality conditions in Arrow–Kurz form. r 2005 Elsevier B.V. All rights reserved. JEL classification: C60; C61

In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The control is applied to the state equation via the boundary and a functional of the control together with the solution of the state equation under such a contro...