non-convex non-smooth optimization

Non-smooth Non-convex Bregman Minimization: Unification and new Algorithms

Published: 2017/07/10, Updated: 2018/01/19

Nonsmooth Optimization bregman minimization, convergence analysis, forward-backward splitting, model functions, non-convex non-smooth optimization, proxdescent

We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate minimizer of the model function yields a descent direction, along which the next iterate is found. Complemented with an Armijo-like line search … Read more

Semidefinite approximations of the polynomial abscissa

Published: 2015/07/30

Didier Henrion

Jean-Bernard Lasserre

Tiên-So'n Pham

Roxana Hess

Control Applications, Nonsmooth Optimization, Semi-definite Programming linear systems control, non-convex non-smooth optimization, polynomial approximations, semialgebraic optimization, semidefinite programming

Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is H\”older continuous, and not locally Lipschitz in general, which is a source of numerical difficulties for designing and optimizing control laws. In … Read more