composite optimization – Page 3 – Optimization Online

An Approximate Lagrange Multiplier Rule

Published: 2009/06/04

Nonsmooth Optimization composite optimization, lagrange multiplier rule, locally lipschitz functions, nonsmooth calculus, subdifferential

In this paper, we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the so-called approximate multiplier rule. In establishing the link between the approximate and the exact multiplier rule we first derive an approximate multiplier rule for a very general class of optimization problems using the … Read more

Identifying Activity

Published: 2009/01/17, Updated: 2011/01/13

Adrian Lewis

Stephen Wright

Constrained Nonlinear Optimization, Nonsmooth Optimization active set, composite optimization, constrained optimization, identification, mangasarian-fromovitz constraint qualification

Identification of active constraints in constrained optimization is of interest from both practical and theoretical viewpoints, as it holds the promise of reducing an inequality-constrained problem to an equality-constrained problem, in a neighborhood of a solution. We study this issue in the more general setting of composite nonsmooth minimization, in which the objective is a … Read more