Related papers: A Convergent Algorithm Based on Deterministic Appr…
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…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
An indefinite stochastic Riccati Equation is a matrix-valued, highly nonlinear backward stochastic differential equation together with an algebraic, matrix positive definiteness constraint. We introduce a new approach to solve a class of…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
In this paper, the known deterministic linear-quadratic Stackelberg game is revisited, whose open-loop Stackelberg solution actually possesses the nature of time inconsistency. To handle this time inconsistency, {a two-tier game framework…
In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially…
This paper is concerned with the deterministic optimal control of Ito stochastic systems with random coefficients. The necessary and sufficient conditions for the unique solvability of the optimal control problem with random coefficients…
In this paper, a leader-follower stochastic differential game is studied for a linear stochastic differential equation with a quadratic cost functional. The coefficients in the state equation and the weighting matrices in the cost…
This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
In this paper, we propose an RADI-type method for large-scale stochastic continuous-time algebraic Riccati equations with sparse and low-rank matrices. This new variant of RADI-type methods is developed by integrating the core concept of…
This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…
One key challenge for solving a general stochastic optimization problem with expectations in the objective and constraint functions using ordinary stochastic iterative methods lies in the infeasibility issue caused by the randomness over…
This work considers a stochastic Nash game in which each player solves a parameterized stochastic optimization problem. In deterministic regimes, best-response schemes have been shown to be convergent under a suitable spectral property…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…
Riccati differential equations is the class of first-order and quadratic ordinary differential equations and has various applications in the systems and control theory. In this paper, we analyze a switched Riccati differential equation that…
We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…
The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…