On Global Optimization

This paper presents a relatively “unfettered” method for finding global optima to constrained nonlinear programs. The method reformulates the given program into a bi-objective mixed-integer program that is then solved for the Nash equilibrium. A numerical example (whose solution provides a new benchmark against which other algorithms may be assessed) is included to illustrate the … Read more

Accelerating block-decomposition first-order methods for solving composite saddle-point and two-player Nash equilibrium problems

This article considers the two-player composite Nash equilibrium (CNE) problem with a separable non-smooth part, which is known to include the composite saddle-point (CSP) problem as a special case. Due to its two-block structure, this problem can be solved by any algorithm belonging to the block-decomposition hybrid proximal-extragradient (BD-HPE) framework. The framework consists of a … Read more

A Block Coordinate Descent Method for Regularized Multi-Convex Optimization with Applications to Nonnegative Tensor Factorization and Completion

This paper considers regularized block multi-convex optimization, where the feasible set and objective function are generally non-convex but convex in each block of variables. We review some of its interesting examples and propose a generalized block coordinate descent method. (Using proximal updates, we further allow non-convexity over some blocks.) Under certain conditions, we show that … Read more

The Price of Atomic Selfish Ring Routing

We study selfish routing in ring networks with respect to minimizing the maximum latency. Our main result is an establishement of constant bounds on the price of stability (PoS) for routing unsplittable flows with linear latency. We show that the PoS is at most 6.83, which reduces to 4:57 when the linear latency functions are … Read more

Smoothing techniques for computing Nash equilibria of sequential games

We develop first-order smoothing techniques for saddle-point problems that arise in the Nash equilibria computation of sequential games. The crux of our work is a construction of suitable prox-functions for a certain class of polytopes that encode the sequential nature of the games. An implementation based on our smoothing techniques computes approximate Nash equilibria for … Read more

Formulation of Oligopolistic Competition in AC Power Networks: An NLP Approach

In this paper, oligopolistic competition in a centralized power market is characterized by a multi-leader single-follower game, and formulated as a nonlinear programming (NLP) problem. An AC network is used to represent the transmission system and is modeled using rectangular coordinates. The follower is composed of a set of competitive suppliers, demands, and the system … Read more

Numerical Study of Affine Supply Function Equilibrium in AC Network-Constrained Markets

An affine supply function equilibrium (SFE) approach is used to discuss voltage constraints and reactive power issues in the modeling of strategic behavior. Generation companies (GenCos) can choose their bid parameters with no restrictions for both energy and spinning reserves. The strategic behavior of generators is formulated as a multi-leader single-follower game. Each GenCo is … Read more

A gradient-based approach for computing Nash equilibria of large sequential games

We propose a new gradient based scheme to approximate Nash equilibria of large sequential two-player, zero-sum games. The algorithm uses modern smoothing techniques for saddle-point problems tailored specifically for the polytopes used in the Nash equilibrium problem. Citation Working Paper, Tepper School of Business, Carnegie Mellon University Article Download View A gradient-based approach for computing … Read more