alternating projections – Optimization Online

Performance Estimation for Smooth and Strongly Convex Sets

Published: 2024/10/18

Convex Optimization, Semi-definite Programming alternating projections, computer-assisted, convex optimization, frank-wolfe, performance estimation problems, semidefinite programming

We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions–known as performance estimation–to apply to structured sets. We prove “interpolation theorems” for smooth and strongly convex sets with Slater points and bounded diameter, showing a wide range of extremal questions amount to structured mathematical programs. Prior function interpolation theorems are recovered … Read more

Global convergence and acceleration of projection methods for feasibility problems involving union convex sets

Published: 2022/02/21, Updated: 2023/07/14

Jan Harold Alcantara

Ching-pei Lee

Complementarity and Variational Inequalities, Nonlinear Optimization, Nonsmooth Optimization alternating projections, averaged projections, fixed point algorithm, global convergence, Linear complementarity problem, nonconvex optimization, proximal methods

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for analyzing global convergence by means of studying fixed-point iterations of a set-valued operator that is the union of … Read more