6 problems

The paper studies safeguarded augmented Lagrangian methods for fully convex composite optimization, including an elastic safeguarding mechanism that enlarges the safeguarding set i…

The AIDAL method is analyzed under assumption (A3) and the finiteness condition $D_h<\infty$, where $D_h$ denotes the relevant Bregman-diameter quantity, and achieves an iteration…

Let $\mathcal{M}^*$ denote the nonempty solution set of $\operatorname{VI}(\theta,\mathcal{J},\mathcal{M})$, where … The proposed P-ALM generates a sequence characterized by an ine…

The methods NL-IAPIAL, QP-AIPP, and iALM are iterative algorithms for solving the optimization problems considered in the paper. Iteration-count conjecture for NL-IAPIAL. NL-IAPIAL…

Augmented-Lagrangian limit conjecture. A similar convergence result can also be verified for the more general case of non-convex nonlinear programming.

The rank-plus-one conjecture for second-order optimality. If $x^*$ is a local minimizer, MFCQ holds at $x^*$, and the rank of…