LOCALLY LIPSCHITZ VECTOR OPTIMIZATION WITH INEQUALITY AND EQUALITY CONSTRAINTS

The present paper studies the following constrained vector optimization problem: min(C) f(x), g(x) is an element of -K, h(x) = 0, where f : R(n) -> R(m), g : R(n) -> R(p) are locally Lipschitz functions, h: R(n) -> R(q) is C(1) function, and C subset of R(m) and K subset of R(p) are closed convex cones. Two types of solutions are important for the consideration, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers of order 1). In terms of the Dini directional derivative first-order necessary conditions for a point x(0) to be a w-minimizer and first-order sufficient conditions for x(0) to be an i-minimizer are obtained. Their effectiveness is illustrated on an example. A comparison with some known results is done.