Quadratic growth and critical point stability of semi-algebraic functions

We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential — a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. Citation 13 pages, September, 2013 Article Download View Quadratic growth and critical point stability of semi-algebraic … Read more

Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential.

We prove that uniform second order growth, tilt stability, and strong metric regularity of the subdifferential — three notions that have appeared in entirely different settings — are all essentially equivalent for any lower-semicontinuous, extended-real-valued function. Citation Cornell University, School of Operations Research and Information Engineering, 206 Rhodes Hall Cornell University Ithaca, NY 14853. May … Read more

Algorithms for the quasiconvex feasibility problem

We study the behavior of subgradient projection algorithms for the quasiconvex feasibility problem of finding a point x^* in R^n that satisfies the inequalities f_i(x^*) less or equal 0, for all i=1,2,…,m, where all functions are continuous and quasiconvex. We consider the consistent case when the solution set is nonempty. Since the Fenchel-Moreau subdifferential might … Read more

Weak Stationarity: Eliminating the Gap between Necessary and Sufficient Conditions

Starting from known necessary extremality conditions in terms of strict subdifferentials and normals the notion of weak stationarity is introduced. It is defined in terms of initial space elements. The necessary conditions become necessary and sufficient (for stationarity). Citation School of Information Technology and Mathematical Sciences, Centre of Information and Applied Optimization, University of Ballarat, … Read more