Related papers: A single-phase, proximal path-following framework

Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…

This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for…

Consider the problem of minimizing the expected value of a (possibly nonconvex) cost function parameterized by a random (vector) variable, when the expectation cannot be computed accurately (e.g., because the statistics of the random…

In this paper, we attempt to compare two distinct branches of research on second-order optimization methods. The first one studies self-concordant functions and barriers, the main assumption being that the third derivative of the objective…

In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…

A framework is introduced for sequentially solving convex stochastic minimization problems, where the objective functions change slowly, in the sense that the distance between successive minimizers is bounded. The minimization problems are…

In this paper we propose a framework to analyze iterative first-order optimization algorithms for time-varying convex optimization. We assume that the temporal variability is caused by a time-varying parameter entering the objective, which…

For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach…

An algorithm framework is proposed for minimizing nonsmooth functions. The framework is variable-metric in that, in each iteration, a step is computed using a symmetric positive definite matrix whose value is updated as in a quasi-Newton…

We study a Newton-like method for the minimization of an objective function that is the sum of a smooth convex function and an l-1 regularization term. This method, which is sometimes referred to in the literature as a proximal Newton…

This paper proposes a provably convergent multiblock ADMM for nonconvex optimization with nonlinear dynamics constraints, overcoming the divergence issue in classical extensions. We consider a class of optimization problems that arise from…

Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is…

We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the…

We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…

In convex optimization, continuous-time counterparts have been a fruitful tool for analyzing momentum algorithms. Fewer such examples are available when the function to minimize is non-convex. In several cases, discrepancies arise between…

In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…

In this paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…

Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…

We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…