This paper is devoted to the theoretical and numerical investigation of an augmented
Lagrangian method for the solution of optimization problems with geometric constraints …

As a starting point of our research, we show that, for a fixed order γ≥ 1, each local minimizer
of a rather general nonsmooth optimization problem in Euclidean spaces is either M …

The optimization literature is vast in papers dealing with improvements on the global
convergence of augmented Lagrangian schemes. Usually, the results are based on weak …

Abstract In Andreani et al.(Weak notions of nondegeneracy in nonlinear semidefinite
programming, 2020), the classical notion of nondegeneracy (or transversality) and …

Polynomial matrix inequalities can be solved using hierarchies of convex relaxations,
pioneered by Henrion and Lassere. In some cases, this might not be practical, and one may …

The growing dependence on optimization models in decision-making has created a demand
for tools that can facilitate the formulation and resolution of a broader range of real-world …

Augmented Lagrangian (AL) algorithms are very popular and successful methods for solving
constrained optimization problems. Recently, global convergence analysis of these methods …

We present new constraint qualification conditions for nonlinear semidefinite programming
that extend some of the constant rank-type conditions from nonlinear programming. As an …

This paper is devoted to studying the stationary solutions of a general constrained
optimization problem through its associated unconstrained penalized problems. We aim to …

Based on the recently introduced Scaled Positive Approximate Karush–Kuhn–Tucker
condition for single objective problems, we derive a sequential necessary optimality …