Noncritical Solution – Optimization Online

New Sufficient and Necessary Conditions for Constrained and Unconstrained Lipschitzian Error Bounds

Published: 2025/03/24

Complementarity and Variational Inequalities, Global Optimization Theory, Nonsmooth Optimization Cone complementarity system, constrained equation, Lipschitzian Error Bound, metric subregularity, Noncritical Solution, Nonsmooth composite equation, Normal qualification condition, subtransversality

Local error bounds play a fundamental role in mathematical programming and variational analysis. They are used e.g. as constraint qualifications in optimization, in developing calculus rules for generalized derivatives in nonsmooth and set-valued analysis, and they serve as a key ingredient in the design and convergence analysis of Newton-type methods for solving systems of possibly … Read more

Sufficient Conditions for Lipschitzian Error Bounds for Complementarity Systems

Published: 2023/08/30

Mario Jelitte

Nonlinear Optimization, Nonsmooth Optimization aubin property, Complementarity System, Lipschitzian Error Bound, metric regularity, Mordukhovich Normal Cone, Noncritical Solution, subtransversality

We are concerned with Lipschitzian error bounds and Lipschitzian stability properties for solutions of a complementarity system. For this purpose, we deal with a nonsmooth slack-variable reformulation of the complementarity system, and study conditions under which the reformulation serves as a local error bound for the solution set of the complementarity system. We also discuss … Read more