Bo Jiang – Optimization Online

Vector Transport-Free SVRG with General Retraction for Riemannian Optimization: Complexity Analysis and Practical Implementation

Published: 2017/05/25, Updated: 2017/05/26

Constrained Nonlinear Optimization, Stochastic Programming matrix completion, orthogonality constraints, principal component analysis, riemannian manifold, stochastic variance reduced gradient

In this paper, we propose a vector transport-free stochastic variance reduced gradient (SVRG) method with general retraction for empirical risk minimization over Riemannian manifold. Existing SVRG methods on manifold usually consider a specific retraction operation, and involve additional computational costs such as parallel transport or vector transport. The vector transport-free SVRG with general retraction we … Read more

hBcnorm regularization algorithms for optimization over permutation matrices

Published: 2015/11/12, Updated: 2018/06/06

Bo Jiang

Ya-Feng Liu

Zaiwen Wen

0-1 Programming, Constrained Nonlinear Optimization barzilai-borwein method, cutting planes, doubly stochastic matrix, negative proximal point, permutation matrix, quadratic assignment problem, regularization

Optimization problems over permutation matrices appear widely in facility layout, chip design, scheduling, pattern recognition, computer vision, graph matching, etc. Since this problem is NP-hard due to the combinatorial nature of permutation matrices, we relax the variable to be the more tractable doubly stochastic matrices and add an $L_p$-norm ($0 < p < 1$) regularization ... Read more

A semi-proximal-based strictly contractive Peaceman-Rachford splitting method

Published: 2015/06/07

Yan Gu

Deren Han

Bo Jiang

Convex and Nonsmooth Optimization convergence rate, convex optimization, peaceman-rachford splitting method, semi-proximal, strictly contractive

The Peaceman-Rachford splitting method is very efficient for minimizing sum of two functions each depends on its variable, and the constraint is a linear equality. However, its convergence was not guaranteed without extra requirements. Very recently, He et al. (SIAM J. Optim. 24: 1011 – 1040, 2014) proved the convergence of a strictly contractive Peaceman-Rachford … Read more

A Framework of Constraint Preserving Update Schemes for Optimization on Stiefel Manifold

Published: 2013/01/01, Updated: 2013/12/25

Yu-Hong Dai

Bo Jiang

Applications - Science and Engineering, Nonlinear Optimization adaptive nonmonotone line search, barzilai-borwein-like method, feasible, global convergence, heterogeneous quadratic functions, kohn-sham total energy minimization, low-rank correlation matrix, null space, orthogonality constraint, range space, sphere constraint, stiefel manifold

This paper considers optimization problems on the Stiefel manifold $X^TX=I_p$, where $X\in \mathbb{R}^{n \times p}$ is the variable and $I_p$ is the $p$-by-$p$ identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of $X$ and the null space of $X^T$. While this general framework … Read more