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We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…
We propose a (seemingly) new computationally tractable model for multi-stage decision making under stochastic uncertainty.
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…
We consider a risk-averse stochastic capacity planning problem under uncertain demand in each period. Using a scenario tree representation of the uncertainty, we formulate a multistage stochastic integer program to adjust the capacity…
We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and detail the Stochastic Dual Dynamic Programming algorithm to…
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…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
We study the problem of designing systems in order to minimize cost while meeting a given flexibility target. Flexibility is attained by enforcing a joint chance constraint, which ensures that the system will exhibit feasible operation with…
Optimal inventory leads to stochastic optimization problems where deterministic delivery decisions have to be made in advance of stochastic demand realizations. Similarly, risk deposits have to be given before the random outcomes of…
Multistage robust optimization problems can be interpreted as two-person zero-sum games between two players. We exploit this game-like nature and utilize a game tree search in order to solve quantified integer programs (QIPs). In this…
Multi-period portfolio optimization is important for real portfolio management, as it accounts for transaction costs, path-dependent risks, and the intertemporal structure of trading decisions that single-period models cannot capture.…
We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…
Multi-stage optimization under uncertainty techniques can be used to solve long-term management problems. Although many optimization modeling language extensions as well as computational environments have been proposed, the acceptance of…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
Uncertainties such as setup and range errors can significantly compromise proton therapy. A discrete uncertainty set is often constructed to represent different uncertainty scenarios. A min-max robust optimization approach is then utilized…
In this paper, we introduce a framework for solving finite-horizon multistage optimization problems under uncertainty in the presence of auxiliary data. We assume the joint distribution of the uncertain quantities is unknown, but noisy…
Multi-stage stochastic optimization lies at the core of decision-making under uncertainty. As the analytical solution is available only in exceptional cases, dynamic optimization aims to efficiently find approximations but often neglects…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…