Related papers: SSNCVX: A primal-dual semismooth Newton method for…

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

We propose several new nonsmooth Newton methods for solving convex composite optimization problems with polyhedral regularizers, while avoiding the computation of complicated second-order information on these functions. Under the…

We provide an overview of primal-dual algorithms for nonsmooth and non-convex-concave saddle-point problems. This flows around a new analysis of such methods, using Bregman divergences to formulate simplified conditions for convergence.

This paper presents the SCvx algorithm, a successive convexification algorithm designed to solve non-convex constrained optimal control problems with global convergence and superlinear convergence-rate guarantees. The proposed algorithm can…

In this paper, we extend our previous results and formally propose the SCvx-fast algorithm, a new addition to the Successive Convexification algorithmic framework. The said algorithm solves non-convex optimal control problems with specific…

A new primal-dual algorithm is presented for solving a class of non-convex minimization problems. This algorithm is based on canonical duality theory such that the original non-convex minimization problem is first reformulated as a…

We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…

Support vector machine (SVM) has proved to be a successful approach for machine learning. Two typical SVM models are the L1-loss model for support vector classification (SVC) and $\epsilon$-L1-loss model for support vector regression (SVR).…

This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…

Clustering may be the most fundamental problem in unsupervised learning which is still active in machine learning research because its importance in many applications. Popular methods like K-means, may suffer from instability as they are…

This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant positive linear dependence…

This paper proposes a new algorithm that solves non-convex optimal control problems with a theoretical guarantee for global convergence to a feasible local solution of the original problem. The proposed algorithm extends the recently…

This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…

We introduce Newton-ADMM, a method for fast conic optimization. The basic idea is to view the residuals of consecutive iterates generated by the alternating direction method of multipliers (ADMM) as a set of fixed point equations, and then…

We introduce two novel primal-dual algorithms for addressing nonconvex, nonconcave, and nonsmooth saddle point problems characterized by the weak Minty Variational Inequality (MVI). The first algorithm, Nonconvex-Nonconcave Primal-Dual…

We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem.…

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

Indicator functions of taking values of zero or one are essential to numerous applications in machine learning and statistics. The corresponding primal optimization model has been researched in several recent works. However, its dual…