scholarly journals Multivariate Spectral Gradient Algorithm for Nonsmooth Convex Optimization Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Yaping Hu
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Nonsmooth Convex Optimization ◽  
Convex Optimization Problem ◽  
Convex Optimization Problems ◽  
Yosida Regularization ◽  
Approximate Function ◽  
Original Objective

We propose an extended multivariate spectral gradient algorithm to solve the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.

scholarly journals Wei-Yao-Liu Conjugate Gradient Algorithm for Nonsmooth Convex Optimization Problems

2020 ◽  
Vol 8 (2) ◽  
pp. 403-413
Author(s):  
Yaping Hu ◽  
Liying Liu ◽  
Yujie Wang
Keyword(s):  
Convex Optimization ◽  
Conjugate Gradient ◽  
Optimization Problems ◽  
Conjugate Gradient Algorithm ◽  
Gradient Algorithm ◽  
Nonsmooth Convex Optimization ◽  
Convex Optimization Problem ◽  
Yosida Regularization ◽  
Global Convergence Property ◽  
Approximate Function

This paper presents a Wei-Yao-Liu conjugate gradient algorithm for nonsmooth convex optimization problem. The proposed algorithm makes use of approximate function and gradient values of the Moreau-Yosida regularization function instead of the corresponding exact values.  Under suitable conditions, the global convergence property could be established for the proposed conjugate gradient  method. Finally, some numerical results are reported to show the efficiency of our algorithm.

scholarly journals An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jie Shen ◽  
Li-Ping Pang ◽  
Dan Li
Keyword(s):  
Convex Optimization ◽  
Objective Function ◽  
Rate Of Convergence ◽  
Nonsmooth Optimization ◽  
Optimization Problem ◽  
Nonsmooth Convex Optimization ◽  
Convex Optimization Problem ◽  
Type Method ◽  
Yosida Regularization ◽  
Quasi Newton

An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.

Counterweight Balancing for Reducing Machine Frame Vibration: A Convex Optimization Framework

2006 ◽  
Author(s):  
Myriam Verschuure ◽  
Bram Demeulenaere ◽  
Jan Swevers ◽  
Joris De Schutter
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Global Optimum ◽  
Convex Optimization Problem ◽  
Optimization Framework ◽  
Convex Optimization Problems ◽  
Drive Speed ◽  
Maximal Reduction

This paper focusses on reducing, through counterweight addition, the vibration of an elastically mounted, rigid machine frame that supports a linkage. In order to determine the counterweights that yield a maximal reduction in frame vibration, a non-linear optimization problem is formulated with the frame kinetic energy as objective function and such that a convex optimization problem is obtained. Convex optimization problems are nonlinear optimization problems that have a unique (global) optimum, which can be found with great efficiency. The proposed methodology is successfully applied to improve the results of the benchmark four-bar problem, first considered by Kochev and Gurdev. For this example, the balancing is shown to be very robust for drive speed variations and to benefit only marginally from using a coupler counterweight.

scholarly journals New inertial proximal gradient methods for unconstrained convex optimization problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Peichao Duan ◽  
Yiqun Zhang ◽  
Qinxiong Bu
Keyword(s):  
Convex Optimization ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Gradient Algorithm ◽  
Proximal Gradient Method ◽  
Proximal Point ◽  
Convex Optimization Problem ◽  
Convex Optimization Problems ◽  
Acceleration Methods ◽  
Weak Convergence Theorem

AbstractThe proximal gradient method is a highly powerful tool for solving the composite convex optimization problem. In this paper, firstly, we propose inexact inertial acceleration methods based on the viscosity approximation and proximal scaled gradient algorithm to accelerate the convergence of the algorithm. Under reasonable parameters, we prove that our algorithms strongly converge to some solution of the problem, which is the unique solution of a variational inequality problem. Secondly, we propose an inexact alternated inertial proximal point algorithm. Under suitable conditions, the weak convergence theorem is proved. Finally, numerical results illustrate the performances of our algorithms and present a comparison with related algorithms. Our results improve and extend the corresponding results reported by many authors recently.

A differential inclusion-based approach for solving nonsmooth convex optimization problems

Optimization ◽  
2013 ◽  
Vol 62 (9) ◽  
pp. 1203-1226 ◽  
Author(s):  
Alireza Hosseini ◽  
S. Mohammad Hosseini ◽  
M. Soleimani-damaneh
Keyword(s):  
Convex Optimization ◽  
Differential Inclusion ◽  
Optimization Problems ◽  
Nonsmooth Convex Optimization ◽  
Convex Optimization Problems
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