1989•Numerical Functional Analysis and OptimizationRequires access

Stability of solutions for a class of nonlinear cone constrained optimization problems, part 1: Basic theory

Walter Alt

Abstract

We Gonsider a class of nonlinear cone constrained optimization problems depending on a parameter. Under the assumption of a constraint qualification, a second order sufficient optimality condition and a stability condition for the Lagrange multipliers it is shown, that for sufficiently smooth perturbations of the constraints and the objective function the optimal solutions obey a type of Lipschitz condition.

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Key concepts: Mathematics, Lipschitz continuity, Cone (formal languages), Class (philosophy), Nonlinear system, Lagrange multiplier, Constraint (computer-aided design), Stability (learning theory)