kl inequality – Optimization Online

From error bounds to the complexity of first-order descent methods for convex functions

Published: 2015/10/27, Updated: 2015/11/02

Convex and Nonsmooth Optimization complexity, compressed sensing, convex optimization, error bound, forward-backward method, kl inequality, lasso

This paper shows that error bounds can be used as effective tools for deriving complexity results for first-order descent methods in convex minimization. In a first stage, this objective led us to revisit the interplay between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can show the equivalence between the two concepts for convex … Read more

Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs

Published: 2014/09/29

Jérôme Bolte

Edouard Pauwels

Applications - Science and Engineering, Nonlinear Optimization converging methods, extended sequential quadratic method, kkt points, kl inequality, moving balls method, nonlinear programming, sequential quadratic programming, sl1qp, tame optimization

In view of solving nonsmooth and nonconvex problems involving complex constraints (like standard NLP problems), we study general maximization-minimization procedures produced by families of strongly convex sub-problems. Using techniques from semi-algebraic geometry and variational analysis –in particular Lojasiewicz inequality– we establish the convergence of sequences generated by this type of schemes to critical points. The … Read more