In this paper we study the nonsmooth semi-infinite programming problem with inequality constraints. First, we consider the notions of local cone approximation $Lambda$ and $Lambda$-subdifferential. Then, we derive the Karush-Kuhn-Tucker optimality conditions under the Abadie and the Guignard constraint qualifications.

Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir ...

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...

1. A competitive equilibrium is a sequence (p * t , c * t , s * t+1) T t=0 such that (i) (c * t , s * t+1) T t=0 solves max (ct,s t+1) T t=0 T t=0 β t u(c t), subject to (1) c t + p * t s t+1 ≤ (p * t + y t)s t , ∀t c t , s t ≥ 0, ∀t s 0 = 1 and (ii) markets clear: c * t = y t , ∀t s * t = 1, ∀t 2. The equation is: p * t = β u (y t+1) u (y t) (p * t+1 + y t+1) Proof: Let (p * t , c * t , s * t+...

It is shown how one can get upper bounds for ju ? vj when u and v are the (viscosity) solutions of ut ? (Dxu))xu = 0 and vt ? (Dxv))xv = 0; respectively, in (0;1) with Dirichlet boundary conditions. Similar results are obtained for some other parabolic equations as well, including certain equations in divergence form. 1. Introduction In this paper we study the problem of how to estimate the dii...

This paper studies a class of problems consisting of minimizing a continuously differentiable function penalizedwith the so-called `0-norm over a symmetric set. These problems are hard to solve, yet prominent in many fields and applications.We first study the proximal mapping with respect to the `0-norm over symmetric sets, and provide an efficient method to attainit. The method is ...

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 note, we prove that the KKT mapping for nonlinear semidefinite optimization problem is upper Lipschitz continuous at the KKT point, under the second-order sufficient optimality conditions and the strict Robinson constraint qualification.

The study of Einstein equations leads naturally to Cauchy problems with initial data on hypersurfaces which closely resemble hyperboloids in Minkowski space-time, and with initial data with polyhomogeneous asymptotics, that is, with asymptotic expansions in terms of powers of ln r and inverse powers of r. Such expansions also arise in the conformal method for analysing wave equations in odd spa...