A Framework of Inertial Alternating Direction Method of Multipliers for Non-Convex Non-Smooth Optimization

In this paper, we propose an algorithmic framework dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our framework employs the general minimization-majorization (MM) principle to update each block of variables so as to not only unify the convergence analysis of previous … Read more

An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization

In this paper, we introduce TITAN, a novel inerTial block majorIzation minimization framework for non-smooth non-convex opTimizAtioN problems. TITAN is a block coordinate method (BCM) that embeds inertial force to each majorization-minimization step of the block updates. The inertial force is obtained via an extrapolation operator that subsumes heavy-ball and Nesterov-type accelerations for block proximal … Read more

Mitigating Interdiction Risk with Fortification

We study a network fortification problem on a directed network that channels single-commodity resources to fulfill random demands delivered to a subset of the nodes. For given a realization of demands, the malicious interdictor would disrupt the network in a manner that would maximize the total demand shortfalls subject to the interdictor’s constraints. To mitigate … Read more

An Inexact Primal-Dual Smoothing Framework for Large-Scale Non-Bilinear Saddle Point Problems

We develop an inexact primal-dual first-order smoothing framework to solve a class of non-bilinear saddle point problems with primal strong convexity. Compared with existing methods, our framework yields a significant improvement over the primal oracle complexity, while it has competitive dual oracle complexity. In addition, we consider the situation where the primal-dual coupling term has … Read more

Inertial Block Mirror Descent Method for Non-Convex Non-Smooth Optimization

In this paper, we propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. We use the general framework of Bregman distance functions to compute the proximal maps. Our method not only allows using two different extrapolation points to evaluate gradients and adding the inertial force, but also takes advantage … Read more

Differential properties of Euclidean projection onto power cone

In this paper, we study differential properties of Euclidean projection onto the power cone $K^{(p,q)}_n=\{(x,y,z)\in \mathbb{R}_+\times \mathbb{R}_+\times \mathbb{R}^n,\norm{z} \leq x^p y^q\}$, where $0< p,q < 1, p+q=1$. Projections onto certain power cones are examples of semismooth but non-strongly-semismooth projection onto a convex cone. Citation Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang ... Read more

Superlinearly convergent smoothing Newton continuation algorithms for variational inequalities over definable sets

In this paper, we use the concept of barrier-based smoothing approximations introduced by Chua and Li to extend various smoothing Newton continuation algorithms to variational inequalities over general closed convex sets X. We prove that when the underlying barrier has a gradient map that is definable in some o-minimal structure, the iterates generated converge superlinearly … Read more