Related papers: The L-Shaped Method for Stochastic Programs with D…
We present StochasticPrograms.jl, a user-friendly and powerful open-source framework for stochastic programming written in the Julia language. The framework includes both modeling tools and structure-exploiting optimization algorithms.…
We study a class of two-stage stochastic programs, namely, those with fixed recourse matrix and fixed costs, and linear second stage. We show that, under mild assumptions, the problem can be solved with just one scenario, which we call an…
We study stochastic mixed integer programs with both first-stage and recourse decisions involving mixed integer variables. A new family of Lagrangian cuts, termed ``ReLU Lagrangian cuts," is introduced by reformulating the nonanticipativity…
This paper introduces a novel multi-stage decision-making model that integrates hypothesis testing and dynamic programming algorithms to address complex decision-making scenarios.Initially,we develop a sampling inspection scheme that…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-order case, we propose a framework of transition from deterministic or…
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
We study a pessimistic stochastic bilevel program in the context of sequential two-player games, where the leader makes a binary here-and-now decision, and the follower responds a continuous wait-and-see decision after observing the…
In this article we study the problem of jointly deciding carsharing prices and vehicle relocations. We consider carsharing services operating in the context of multi-modal urban transportation systems. Pricing decisions take into account…
We study two classic variants of block-structured integer programming. Two-stage stochastic programs are integer programs of the form $\{A_i \mathbf{x} + D_i \mathbf{y}_i = \mathbf{b}_i\textrm{ for all }i=1,\ldots,n\}$, where $A_i$ and…
Real-world distributed systems and networks are often unreliable and subject to random failures of its components. Such a stochastic behavior affects adversely the complexity of optimization tasks performed routinely upon such systems, in…
We study stochastic optimization problems with objective function given by the expectation of the maximum of two linear functions defined on the component random variables of a multivariate Gaussian distribution. We consider random…
In this paper the problem of selecting $p$ out of $n$ available items is discussed, such that their total cost is minimized. We assume that costs are not known exactly, but stem from a set of possible outcomes. Robust recoverable and…
We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…
This paper applies the N-block PCPM algorithm to solve multi-scale multi-stage stochastic programs, with the application to electricity capacity expansion models. Numerical results show that the proposed simplified N-block PCPM algorithm,…
In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…
Uncertain optimization problems with decision dependent information discovery allow the decision maker to control the timing of information discovery, in contrast to the classic multistage setting where uncertain parameters are revealed…
We study multistage distributionally robust mixed-integer programs under endogenous uncertainty, where the probability distribution of stage-wise uncertainty depends on the decisions made in previous stages. We first consider two ambiguity…
We propose a two-stage penalized least squares method to build large systems of structural equations based on the instrumental variables view of the classical two-stage least squares method. We show that, with large numbers of endogenous…
We examine a multi-stage stochastic optimization problem characterized by stagewise-independent, decision-dependent noises with strict constraints. The problem assumes convexity in that, following a specific relaxation, it transforms into a…