kkt points – Optimization Online

Optimal Nonergodic Primal-Dual Complexity of Efficient Inexact Parameter-Free Augmented Lagrangian Methods

Published: 2026/08/04, Updated: 2026/08/10

Augmented Lagrangian (AL) methods are a classical framework for constrained optimization, but for directly verifiable approximate KKT points, known first-order complexity bounds for standard inexact AL methods are suboptimal, while the best known proximal augmented Lagrangian (PAL) bounds retain an additional logarithmic factor. We consider linearly constrained convex composite problems with a smooth convex term … Read more

ASPEN: An Additional Sampling Penalty Method for Finite-Sum Optimization Problems with Nonlinear Equality Constraints

Published: 2025/08/08

Nonlinear Optimization, Stochastic Approaches, Stochastic Programming Additional sampling, almost-sure convergence, constrained optimization, kkt points, non-monotone line search, penalty functions, sample average approximation

We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework of quadratic penalty methods. Thus, depending on the problem at hand, the resulting method may exhibit a sample size strategy ranging from a mini-batch on one … Read more

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

Published: 2014/09/29

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