Related papers: Minimax Problems with Coupled Linear Constraints: …
Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…
We consider a linear relaxation of a generalized minimum-cost network flow problem with binary input dependencies. In this model the flows through certain arcs are bounded by linear (or more generally, piecewise linear concave) functions of…
We propose and analyze a general framework called nonlinear preconditioned primal-dual with projection for solving nonconvex-nonconcave and non-smooth saddle-point problems. The framework consists of two steps. The first is a nonlinear…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in…
This paper proposes an asymmetric perturbation technique for solving bilinear saddle-point optimization problems, commonly arising in minimax problems, game theory, and constrained optimization. Perturbing payoffs or values is known to be…
Recently, min-max optimization problems have received increasing attention due to their wide range of applications in machine learning (ML). However, most existing min-max solution techniques are either single-machine or distributed…
Decentralized minimax optimization has been actively studied in the past few years due to its application in a wide range of machine learning models. However, the current theoretical understanding of its convergence rate is far from…
In this paper, we study a joint bandwidth allocation and path selection problem via solving a multi-objective minimization problem under the path cardinality constraints, namely MOPC. Our problem formulation captures various types of…
The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…
Traditional network interdiction problems focus on removing vertices or edges from a network so as to disconnect or lengthen paths in the network; network diversion problems seek to remove vertices or edges to reroute flow through a…
In the multiuser downlink, power allocation for linear precoders that minimize the sum of mean squared errors under a sum power constraint is a non-convex problem. Many existing algorithms solve an equivalent convex problem in the virtual…
We develop primal-dual coordinate methods for solving bilinear saddle-point problems of the form $\min_{x \in \mathcal{X}} \max_{y\in\mathcal{Y}} y^\top A x$ which contain linear programming, classification, and regression as special cases.…
Compared to ordinary function minimization problems, min-max optimization algorithms encounter far greater challenges because of the existence of periodic cycles and similar phenomena. Even though some of these behaviors can be overcome in…
Saddle-point problems appear in various settings including machine learning, zero-sum stochastic games, and regression problems. We consider decomposable saddle-point problems and study an extension of the alternating direction method of…
The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
In this paper, the distributed strongly convex optimization problem is studied with spatio-temporal compressed communication and equality constraints. For the case where each agent holds an distributed local equality constraint, a…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…