locally lipschitz functions – Optimization Online

Proximal Point Method for Minimizing Quasiconvex Locally Lipschitz Functions on Hadamard Manifolds

Published: 2012/02/07

Global Optimization global convergence, hadamard manifolds, locally lipschitz functions, proximal point algorithm, quasiconvex functions

In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the … Read more

An Approximate Lagrange Multiplier Rule

Published: 2009/06/04

Joydeep Dutta

Suvendu Pattanaik

Michel Thera

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