Related papers: Exact Worst-case Performance of First-order Method…

In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…

We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…

We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…

Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…

Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…

Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…

We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…

In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…

Quasar-convex functions form a broad nonconvex class with applications to linear dynamical systems, generalized linear models, and Riemannian optimization, among others. Current nearly optimal algorithms work only in affine spaces due to…

We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem…

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function,…

We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…

We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…

We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…

We propose a first order algorithm, a modified version of FISTA, to solve an optimization problem with an objective function that is a sum of a possibly nonconvex function, with Lipschitz continuous gradient, and a convex function which can…

A strategy is proposed for characterizing the worst-case performance of algorithms for solving nonconvex smooth optimization problems. Contemporary analyses characterize worst-case performance by providing, under certain assumptions on an…

Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…

We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…

We consider stochastic convex optimization problems with affine constraints and develop several methods using either primal or dual approach to solve it. In the primal case, we use a special penalization technique to make the initial…