Related papers: An exact dynamic programming algorithm, lower and …
We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
We apply numerical dynamic programming techniques to solve discrete-time multi-asset dynamic portfolio optimization problems with proportional transaction costs and shorting/borrowing constraints. Examples include problems with multiple…
Portfolio optimization is an important process in finance that consists in finding the optimal asset allocation that maximizes expected returns while minimizing risk. When assets are allocated in discrete units, this is a combinatorial…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is…
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…
A very simple example of an algorithmic problem solvable by dynamic programming is to maximize, over sets A in {1,2,...,n}, the objective function |A| - \sum_i \xi_i 1(i \in A,i+1 \in A) for given \xi_i > 0. This problem, with random…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
We establish the existence of minimizers in a rather general setting of dynamic stochastic optimization without assuming either convexity or coercivity of the objective function. We apply this to prove the existence of optimal portfolios…
In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a…
In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are "pure" in that they only perform basic operations, as min, max, +, but…
Many sequential decision problems can be formulated as Markov Decision Processes (MDPs) where the optimal value function (or cost-to-go function) can be shown to satisfy a monotone structure in some or all of its dimensions. When the state…
We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019)…
We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a dynamic programming formulation that is…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…