Saddle point criteria for second order $\eta$-approximated vector optimization problems

L ∞ - convergence of saddle - point approximations for second order problems

Saddle Point Seeking for Convex Optimization Problems

In this paper, we consider convex optimization problems with constraints. By combining the idea of a Lie bracket approximation for extremum seeking systems and saddle point algorithms, we propose a feedback which steers a single-integrator system to the set of saddle points of the Lagrangian associated to the convex optimization problem. We prove practical uniform asymptotic stability of the se...

Generalized second-order contingent epiderivatives in parametric vector optimization problems

This paper is concerned with generalized second-order contingent epiderivatives of frontier and solution maps in parametric vector optimization problems. Under some mild conditions, we obtain some formulas for computing generalized second-order contingent epiderivatives of frontier and solution maps, respectively. We also give some examples to illustrate the corresponding results.

Duality Theorem and Vector Saddle Point Theorem for Robust Multiobjective Optimization Problems

In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.

Randomized First-Order Methods for Saddle Point Optimization

In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an O(1/N) and O(1/N) rate of convergence, respectively, for general bilinear saddle point and smooth bilinear saddle point problems based on a new prima-dual termination criterion, and each iteration of ...