In this paper we present SDDP.jl, an open-source library for solving multistage stochastic optimization problems using the Stochastic Dual Dynamic Programming algorithm. SDDP.jl is built upon JuMP, an algebraic modelling language in Julia. This enables a high-level interface for the user, while simultaneously providing performance that is similar to implementations in low-level languages. We benchmark … Read more
We propose an algorithm based on infeasible irreducible subsystems (IIS) to solve general binary chance-constrained problems. By leverag- ing on the problem structure we are able to generate good quality upper bounds to the optimal value early in the algorithm, and the discrete do- main is used to guide us eciently in the search of … Read more
In this paper, we consider a class of finite-sum convex optimization problems defined over a distributed multiagent network with $m$ agents connected to a central server. In particular, the objective function consists of the average of $m$ ($\ge 1$) smooth components associated with each network agent together with a strongly convex term. Our major contribution … Read more
We consider an n-player non-cooperative game with random payoffs and continuous strategy set for each player. The random payoffs of each player are defined using a finite dimensional random vector. We formulate this problem as a chance-constrained game by defining the payoff function of each player using a chance constraint. We first consider the case … Read more
Chance constrained programming, quantile/Value-at-Risk (VaR) optimization and integral quantile / Conditional Value-at-Risk (CVaR) optimization problems as Stochastic Programming Problems with Probability Functions (SPP-PF) are one of the most widely studied optimization problems in recent years. As a rule real-life SPP-PF is nonsmooth nonconvex optimization problem with complex geometry of objective function. Moreover, often it cannot … Read more
In the analysis of complex stochastic dynamic programs, we often seek strong theoretical guarantees on the suboptimality of heuristic policies. One technique for obtaining performance bounds is perfect information analysis: this approach provides bounds on the performance of an optimal policy by considering a decision maker who has access to the outcomes of all future … Read more
We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of Benson’s algorithm to solve this problem. Using Lagrangian duality, we develop scenario-wise decomposition methods to solve the two scalarization problems appearing in Benson’s algorithm. … Read more
Uses of drones and unmanned vehicles (UAVs) in ground or aerial are increasing in both civil and military applications. This paper develops a two-stage stochastic optimization model with a recourse for a multiple drone-routing problem with fuel constraints under uncertainty for the travel between any pair of targets/refueling-sites/depot. We are given a set of n … Read more
We introduce DASC, a decomposition method akin to Stochastic Dual Dynamic Programming (SDDP) which solves some multistage stochastic optimization problems having strongly convex cost functions. Similarly to SDDP, DASC approximates cost-to-go functions by a maximum of lower bounding functions called cuts. However, contrary to SDDP, the cuts computed with DASC are quadratic functions. We also … Read more
We study a class of stochastic programs where some of the elements in the objective function are random, and their probability distribution has unknown parameters. The goal is to find a good estimate for the optimal solution of the stochastic program using data sampled from the distribution of the random elements. We investigate two common … Read more