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Convex quadratic programming (QP) is an essential class of optimization problems with broad applications across various fields. Traditional QP solvers, typically based on simplex or barrier methods, face significant scalability challenges.…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
In this paper, we introduce a \textit{Bi-level OPTimization} (BiOPT) framework for minimizing the sum of two convex functions, where both can be nonsmooth. The BiOPT framework involves two levels of methodologies. At the upper level of…
We prove complexity bounds for the primal-dual algorithm with random extrapolation and coordinate descent (PURE-CD), which has been shown to obtain good practical performance for solving convex-concave min-max problems with bilinear…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…
In this paper, we investigate the continuous time partial primal-dual gradient dynamics (P-PDGD) for solving convex optimization problems with the form $ \min\limits_{x\in X,y\in\Omega}\ f({x})+h(y),\ \textit{s.t.}\ A{x}+By=C $, where $…
This paper proposes TriPD, a new primal-dual algorithm for minimizing the sum of a Lipschitz-differentiable convex function and two possibly nonsmooth convex functions, one of which is composed with a linear mapping. We devise a randomized…
"Classical" First Order (FO) algorithms of convex optimization, such as Mirror Descent algorithm or Nesterov's optimal algorithm of smooth convex optimization, are well known to have optimal (theoretical) complexity estimates which do not…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by the number of function and gradient evaluations. To achieve…
We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core…
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…
We develop a first-order accelerated algorithm for a class of constrained bilinear saddle-point problems with applications to network systems. The algorithm is a modified time-varying primal-dual version of an accelerated mirror-descent…
We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for…
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…
Stochastic nonconvex-concave min-max saddle point problems appear in many machine learning and control problems including distributionally robust optimization, generative adversarial networks, and adversarial learning. In this paper, we…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…
In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…