Rapidly Convergent Algorithms for Nonsmooth Optimization.

Distributed Nonsmooth Optimization with Consensus and Inequality Constraints via Distributed Smooth Proximal-Splitting Algorithm

2020 IEEE 16th International Conference on Control & Automation (ICCA) ◽

10.1109/icca51439.2020.9264474 ◽

2020 ◽

Author(s):

Yue Wei ◽

Hao Fang ◽

Lihua Dou ◽

Qingkai Yang

Keyword(s):

Nonsmooth Optimization ◽

Inequality Constraints ◽

Splitting Algorithm

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A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

Journal of Mathematics ◽

10.1155/2013/750834 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10

Author(s):

Hamid Reza Erfanian ◽

M. H. Noori Skandari ◽

A. V. Kamyad

Keyword(s):

Nonsmooth Optimization ◽

Optimization Problems ◽

Piecewise Linear ◽

Linear Optimization ◽

Optimal Solution ◽

Piecewise Linear Function ◽

Nonsmooth Equations ◽

Smooth Functions ◽

Generalized Derivative ◽

Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

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Nonsmooth Optimization Method for Image Restoration

Volume 3C: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration Control, Analysis, and Identification ◽

10.1115/detc1995-0673 ◽

1995 ◽

Author(s):

Kazufumi Ito ◽

Karl Kunisch

Keyword(s):

Image Restoration ◽

Nonsmooth Optimization ◽

Numerical Optimization ◽

Augmented Lagrangian ◽

Energy Criterion ◽

Optimization Methods ◽

Optimization Method ◽

Augmented Lagrangian Methods ◽

Active Set ◽

First Order

Abstract In this paper we discuss applications of the numerical optimization methods for nonsmooth optimization, developed in [IK1] for the variational formulation of image restoration problems involving bounded variation type energy criterion. The Uzawa’s algorithm, first order augmented Lagrangian methods and Newton-like update using the active set strategy are described.

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