A trust region algorithm with adaptive cubic regularization methods for nonsmooth convex minimization

Authors:
Sha Lu;Zengxin Wei;Lue Li
Affiliations:
School of Mathematics and Information Science, Guangxi University, Nanning, China and School of Mathematical Science, Guangxi Teachers Education University, Nanning, China;School of Mathematics and Information Science, Guangxi University, Nanning, China;School of Mathematical Sciences, Guangxi Normal University, Guilin, China
Venue:
Computational Optimization and Applications
Year:
2012

Citing 19
Cited 0

A nonsmooth version of Newton's method

Mathematical Programming: Series A and B
Convergence analysis of some algorithms for solving nonsmooth equations

Mathematics of Operations Research
A trust region algorithm for minimization of locally Lipschitzian functions

Mathematical Programming: Series A and B
Convergence of some algorithms for convex minimization

Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
A globally convergent Newton method for convex SC1minimization problems

Journal of Optimization Theory and Applications
A family of variable metric proximal methods

Mathematical Programming: Series A and B
A unified approach to global convergence of trust region methods for nonsmooth optimization

Mathematical Programming: Series A and B
Proximal level bundle methods for convex nondifferentiable optimization, saddle-point problems and variational inequalities

Mathematical Programming: Series A and B
Convergence analysis of some methods for minimizing a nonsmooth convex function

Journal of Optimization Theory and Applications
Globally convergent variable metric method for convex nonsmooth unconstrained minimization

Journal of Optimization Theory and Applications
Trust-region methods

Trust-region methods
A Globally and Superlinearly Convergent Algorithm for Nonsmooth Convex Minimization

SIAM Journal on Optimization
Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries

SIAM Journal on Optimization
Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization

Mathematical Programming: Series A and B
Cubic regularization of Newton method and its global performance

Mathematical Programming: Series A and B
Accelerating the cubic regularization of Newton’s method on convex problems

Mathematical Programming: Series A and B
Lagrangian-Dual Functions and Moreau-Yosida Regularization

SIAM Journal on Optimization
Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results

Mathematical Programming: Series A and B
Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity

Mathematical Programming: Series A and B

Quantified Score

Hi-index	0.00

Visualization

Abstract

By using the Moreau-Yosida regularization and proximal method, a new trust region algorithm is proposed for nonsmooth convex minimization. A cubic subproblem with adaptive parameter is solved at each iteration. The global convergence and Q-superlinear convergence are established under some suitable conditions. The overall iteration bound of the proposed algorithm is discussed. Preliminary numerical experience is reported.