Related papers: Dynamic programming in convex stochastic optimizat…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
We consider stochastic optimal control of linear dynamical systems with additive non-Gaussian disturbance. We propose a novel, sampling-free approach, based on Fourier transformations and convex optimization, to cast the stochastic optimal…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
We present an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities in a discrete time setup using theory of dynamic acceptability indices. In the first part of the paper we develop the theory of…
In this paper, we examine the convergence properties of heavy-ball dynamics with Hessian-driven damping in smooth non-convex optimization problems satisfying a {\L}ojasiewicz condition. In this general setting, we provide a series of tight,…
We consider a deterministic continuous time model of monopolistic firm, which chooses production and pricing strategies of a single good. Firm's goal is to maximize the discounted profit over infinite time horizon. The no-backlogging…
This work introduces a sequential convex programming framework for non-linear, finite-dimensional stochastic optimal control, where uncertainties are modeled by a multidimensional Wiener process. We prove that any accumulation point of the…
This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…
The last decade witnessed a rise in the importance of supervised learning applications involving {\em big data} and {\em big models}. Big data refers to situations where the amounts of training data available and needed causes difficulties…
This letter deals with the optimization problems of stochastic switching buffer networks, where the switching law is governed by Markov process. The dynamical buffer network is introduced, and its application in modeling the car-sharing…
We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. The zeroth-order "coefficient"…
An extended quadratic function is a quadratic function plus the indicator function of an affine set, that is, a quadratic function with embedded linear equality constraints. We show that, under some technical conditions, random convex…
This paper proposes an algorithm for solving structured optimization problems, which covers both the backward-backward and the Douglas-Rachford algorithms as special cases, and analyzes its convergence. The set of fixed points of the…
This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
We consider smooth stochastic convex optimization problems in the context of algorithms which are based on directional derivatives of the objective function. This context can be considered as an intermediate one between derivative-free…
This paper investigates the robust optimal control of sampled-data stochastic systems with multiplicative noise and distributional ambiguity. We consider a class of discrete-time optimal control problems where the controller \emph{jointly}…
Data-driven predictive control methods based on the Willems' fundamental lemma have shown great success in recent years. These approaches use receding horizon predictive control with nonparametric data-driven predictors instead of…
We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems contains constrained convex non-smooth optimization problems,…
Convex optimization is a well-established research area with applications in almost all fields. Over the decades, multiple approaches have been proposed to solve convex programs. The development of interior-point methods allowed solving a…