Convergence analysis of an ALF-based nonconvex splitting algorithm with SQP structure

Global Convergence of Splitting Methods for Nonconvex Composite Optimization

We consider the problem of minimizing the sum of a smooth function h with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function P and a surjective linear map M, with the proximal mappings of τP , τ > 0, simple to compute. This problem is nonconvex in general and encompasses many important applications in engineering and mach...

An Alternating Proximal Splitting Method with Global Convergence for Nonconvex Structured Sparsity Optimization

In many learning tasks with structural properties, structured sparse modeling usually leads to better interpretability and higher generalization performance. While great efforts have focused on the convex regularization, recent studies show that nonconvex regularizers can outperform their convex counterparts in many situations. However, the resulting nonconvex optimization problems are still ch...

On the Global Convergence of a Filter--SQP Algorithm

Convergence analysis of an iterative algorithm for the extended regularized nonconvex variational inequalities

In this paper, we suggest and analyze a new system of extended regularized nonconvex variational inequalities and prove the equivalence between the aforesaid system and a fixed point problem. We introduce a new perturbed projection iterative algorithm with mixed errors to find the solution of the system of extended regularized nonconvex variational inequalities. Furthermore, under moderate assu...

Convergence Analysis of Alternating Nonconvex Projections

We consider the convergence properties for alternating projection algorithm (a.k.a alternating projections) which has been widely utilized to solve many practical problems in machine learning, signal and image processing, communication and statistics since it is a gradient-free method (without requiring tuning the step size) and it usually converges fast for solving practical problems. Although...