Related papers: On construction of splitting contraction algorithm…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
Finding a point in the intersection of a collection of closed convex sets, that is the convex feasibility problem, represents the main modeling strategy for many computational problems. In this paper we analyze new stochastic reformulations…
We address the solution of time-varying optimization problems characterized by the sum of a time-varying strongly convex function and a time-invariant nonsmooth convex function. We design an online algorithmic framework based on…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
In this paper we describe a systematic procedure to analyze the convergence of degenerate preconditioned proximal point algorithms. We establish weak convergence results under mild assumptions that can be easily employed in the context of…
He and Yuan's prediction-correction framework [SIAM J. Numer. Anal. 50: 700-709, 2012] is able to provide convergent algorithms for solving separable convex optimization problems at a rate of $O(1/t)$ ($t$ represents iteration times) in…
We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…