The value function approach to convergence analysis in composite\n optimization

2016/04/06 by Edouard Pauwels, Pauwels, Edouard
Mathematics · Computer Science · Engineering · #Advanced Optimization Algorithms Research #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1604.01654

Abstract

This works aims at understanding further convergence properties of first\norder local search methods with complex geometries. We focus on the composite\noptimization model which unifies within a simple formalism many problems of\nthis type. We provide a general convergence analysis of the composite\nGauss-Newton method under tameness assumptions (an extension of\nsemi-algebraicity). Tameness is a very general condition satisfied by virtually\nall problems solved in practice. The analysis is based on recent progresses in\nunderstanding convergence properties of sequential convex programming methods\nthrough the value function.\n

Citations

• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
• SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems

Related

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• On the local convergence of the semismooth Newton method for composite optimization
• Line Search and Trust-Region Methods for Convex-Composite Optimization
• Optimized methods for composite optimization: a reduction perspective
• Local Convergence Analysis of ADMM for Nonconvex Composite Optimization