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Quadratic regularization projected alternating Barzilai--Borwein method for constrained optimization

Yakui Huang(huangyakui2006***at***gmail.com)
Hongwei Liu(hwliu***at***mail.xidian.edu.cn)
Sha Zhou(zhoushamath520***at***gmail.com)

Abstract: In this paper, based on the regularization techniques and projected gradient strategies, we present a quadratic regularization projected alternating Barzilai--Borwein (QRPABB) method for minimizing differentiable functions on closed convex sets. We show the convergence of the QRPABB method to a constrained stationary point for a nonmonotone line search. When the objective function is convex, we prove the error in the objective function at iteration $k$ is bounded by $a/(k+1)$ for some $a$ independent of $k$. Moreover, if the objective function is strongly convex, then the convergence rate is $R$-linear. Numerical comparisons of methods on box-constrained quadratic problems and nonnegative matrix factorization problems show that the QRPABB method is promising.

Keywords: Constrained optimization, Projected Barzilai--Borwein method, Quadratic regularization, Linear convergence, Nonnegative matrix factorization

Category 1: Nonlinear Optimization

Category 2: Applications -- Science and Engineering

Citation:

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Entry Submitted: 08/18/2014
Entry Accepted: 08/18/2014
Entry Last Modified: 08/18/2014

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