Open AccessBook
Optimization and nonsmooth analysis
TLDR
The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
Citations
More filters
Journal ArticleDOI
Smoothing Nonlinear Conjugate Gradient Method for Image Restoration Using Nonsmooth Nonconvex Minimization
Xiaojun Chen,Weijun Zhou +1 more
TL;DR: A smoothing nonlinear conjugate gradient method where an intelligent scheme is used to update the smoothing parameter at each iteration and guarantees that any accumulation point of a sequence generated by this method is a Clarke stationary point of the nonsmooth and nonconvex optimization problem.
Journal ArticleDOI
An Efficient Inexact Symmetric Gauss-Seidel Based Majorized ADMM for High-Dimensional Convex Composite Conic Programming
TL;DR: The results show that for the vast majority of the tested problems, the sGS-imsPADMM is 2–3 times faster than the directly extended multi-block ADMM with the aggressive step-length of 1.618, which is currently the benchmark among first-order methods for solving multi- block linear and quadratic SDP problems though its convergence is not guaranteed.
Journal ArticleDOI
Historical developments in convergence analysis for Newton's and Newton-like methods
TL;DR: In this paper, historical developments in convergence theory as well as error estimates for Newton's method and Newton-like methods for nonlinear equations are described, mainly for differentiable equations in Banach spaces.
Journal ArticleDOI
Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints
TL;DR: Various exact penalty functions for mathematical programs subject to equilibrium constraints are derived, and stationary points of these programs are characterized.
Journal ArticleDOI
Penalty Dual Decomposition Method for Nonsmooth Nonconvex Optimization—Part I: Algorithms and Convergence Analysis
Qingjiang Shi,Mingyi Hong +1 more
TL;DR: An algorithm named penalty dual decomposition (PDD) is proposed for these difficult problems and its various applications are discussed and its performance is evaluated by customizing it to three applications arising from signal processing and wireless communications.