We consider a nonlinear fractional programming problem with inequality constraints, where the functions involved are ρ-semilocally b-preinvex, ρ-semilocally explicitly b-preinvex, ρ-semilocally quasi b-preinvex, ρ-semilocally pseudo bpreinvex and ρ-semi-locally strongly pseudo b-preinvex functions. Necessary optimality conditions are obtained in terms of the right derivative of a function along...

Newton methods of the linesearch type for large-scale minimization subject to linear inequality constraints are discussed. The purpose of the paper is twofold: (i) to give an active–settype method with the ability to delete multiple constraints simultaneously and (ii) to give a relatively short general convergence proof for such a method. It is also discussed how multiple constraints can be add...

Received: date / Revised version: date Abstract. We consider robust semi-definite programs which depend polynomially or rationally on some uncertain parameter that is only known to be contained in a set with a polynomial matrix inequality description. On the basis of matrix sum-of-squares decompositions, we suggest a systematic procedure to construct a family of linear matrix inequality relaxat...

We introduce and analyze an exterior-point method (epm) for constrained optimization problems with both inequality constraints and equations. We show that under the standard second-order optimality conditions the epm converges to the primal-dual solution with 1.5-Q-superlinear rate.

In this paper, we establish a Farkas-Minkowski type alternative theorem under the supposition of nearly semiconvexlike set-valued maps. Based on the alternative theorem and some other lemmas, we present necessary optimality conditions and sufficient optimality conditions for set-valued vector optimization problems with extended inequality constraints in a sense of weak E-minimizers.

This paper deals with optimal control problems for systems affine in the control variable. We have nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we get a second order sufficient condition for the scalar control case. The results use in an essential way t...

Dual characterizations of the containment of a convex set with quasiconvex inequality constraints are investigated. A new Lagrange-type duality and a new closed cone constraint qualification are described, and it is shown that this constraint qualification is the weakest constraint qualification for the duality.

We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz–John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new pr...

For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this...

L 2 boundary decay properties of the heat kernel and spectral density. We deduce bounds on the rate of convergence of the eigenvalues when the region is slightly reduced in size. It is remarkable that several of the bounds do not involve the space dimension. AMS subject classifications: 35P99, 35P20, 47A75, 47B25 keywords: boundary decay, Laplacian, Hardy inequality, eigenfunctions, heat kernel...