Related papers: A primal-dual price-optimization method for comput…
We present an improved combinatorial algorithm for the computation of equilibrium prices in the linear Arrow-Debreu model. For a market with $n$ agents and integral utilities bounded by $U$, the algorithm runs in $O(n^7 \log^3 (nU))$ time.…
Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…
We propose a new methodology to compute equilibria for general equilibrium problems on exchange economies with real financial markets, home-production, and retention. We demonstrate that equilibrium prices can be determined by solving a…
We consider infinite dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the super-replication cost.…
We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated,…
We consider Cournot mean field games of controls, a model originally developed for the production of an exhaustible resource by a continuum of producers. We prove uniqueness of the solution under general assumptions on the price function.…
We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company…
This paper introduces the Minimum Price Markov Game (MPMG), a theoretical model that reasonably approximates real-world first-price markets following the minimum price rule, such as public auctions. The goal is to provide researchers and…
We propose a new pricing strategy for column generation (CG), referred to as Template pricing. This method is motivated by the desire to coordinate solutions of different pricing subproblems in order to accelerate the convergence of the CG…
We propose a real-time nodal pricing mechanism for cost minimization and voltage control in a distribution network with autonomous distributed energy resources and analyze the resulting market using stochastic game theory. Unlike existing…
We present a new primal-dual algorithm for computing the value of the Lagrangian dual of a stochastic mixed-integer program (SMIP) formed by relaxing its nonanticipativity constraints. This dual is widely used in decomposition methods for…
We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between…
In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a…
This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…
In the presence of non-convexities, the power market may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, to achieve an economically stable outcome, the uplift…
This paper presents a novel data-driven approach for approximating the $\varepsilon$-Nash equilibrium in continuous-time linear quadratic Gaussian (LQG) games, where multiple agents interact with each other through their dynamics and…
This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is…
The paper proposes a variational-inequality based primal-dual dynamic that has a globally exponentially stable saddle-point solution when applied to solve linear inequality constrained optimization problems. A Riemannian geometric framework…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…
This paper establishes a primal-dual formulation for continuous-time mean field games (MFGs) and provides a complete analytical characterization of the set of all Nash equilibria (NEs). We first show that for any given mean field flow, the…