相关论文: Regularized two-stage stochastic variational inequ…
In competitive multi-player interactions, simultaneous optimality is a key requirement for establishing strategic equilibria. This property is explicit when the game-theoretic equilibrium is the simultaneously optimal solution of coupled…
We study stochastic Nash equilibrium problems subject to heterogeneous uncertainty on the expected valued cost functions of the individual agents, where we assume no prior knowledge of the underlying probability distributions of the…
We investigate the convergence of symmetric stochastic differential games with interactions via control, where the volatility terms of both idiosyncratic and common noises are controlled. We apply the stochastic maximum principle, following…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs with equilibrium constraints, the equilibrium constraints have…
In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the…
In this work, we study the distributed Nash equilibrium seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A distributed regularized penalty method is proposed. The…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
We study a mean field game problem arising from the production control for multiple firms with price stickiness in the commodity market. The price dynamics for each firm is described as a (controlled) jump-diffusion process with mean-field…
In this paper we extend the well-known L-Shaped method to solve two-stage stochastic programming problems with decision-dependent uncertainty. The method is based on a novel, unifying, formulation and on distribution-specific optimality and…
The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal…
In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…
Transmission system operators employ reserves to deal with unexpected variations of demand and generation to guarantee the security of supply. The French transmission system operator RTE dynamically sizes the required margins using a…
We derive an algorithm in the spirit of Rogers and Davis & Burstein that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recently obtained in the work of Guyon & Henry-Labord\`ere. We…
We present a new Progressive Hedging Algorithm to solve Stochastic Variational Inequalities in the formulation introduced by Rockafellar and Wets in 2017, allowing the generated subproblems to be approximately solved with an implementable…
Optimality conditions in the form of a variational inequality are proved for a class of constrained optimal control problems of stochastic differential equations. The cost function and the inequality constraints are functions of the…
We introduce a new algorithm for the numerical computation of Nash equilibria of competitive two-player games. Our method is a natural generalization of gradient descent to the two-player setting where the update is given by the Nash…
We consider a two-dimensional stochastic heat equation with noise correlated at scale $\rho \ll 1$ and of strength $|\log\rho|^{-1/2}\sigma(v)$ depending nonlinearly on the solution $v$. Under certain conditions, the first author and Gu…
This paper considers a stochastic Nash game in which each player minimizes an expectation valued composite objective. We make the following contributions. (I) Under suitable monotonicity assumptions on the concatenated gradient map, we…
In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate…