Related papers: Multistage Distributionally Robust Mixed-Integer P…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
Mixed-Integer Linear Programming (MILP) is a foundational tool for complex decision-making problems. However, the NP-hard nature of MILP presents a significant computational challenge, motivating the development of machine learning-based…
This paper introduces a node formulation for multistage stochastic programs with endogenous (i.e., decision-dependent) uncertainty. Problems with such structure arise when the choices of the decision maker determine a change in the…
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…
Recent road trials have shown that guaranteeing the safety of driving decisions is essential for the wider adoption of autonomous vehicle technology. One promising direction is to pose safety requirements as planning constraints in…
Mixed-Integer Linear Programming (MILP) is a powerful framework used to address a wide range of NP-hard combinatorial optimization problems, often solved by Branch and Bound (B&B). A key factor influencing the performance of B&B solvers is…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
The unit commitment with transmission constraints in the alternating-current (AC) model is a challenging mixed-integer non-linear optimisation problem. We present an approach based on decomposition of a Mixed-Integer Semidefinite…
The necessity to deal with uncertain data is a major challenge in decision making. Robust optimization emerged as one of the predominant paradigms to produce solutions that hedge against uncertainty. In order to obtain an even more…
We study the computational complexity of multi-stage robust optimization problems. Such problems are formulated with alternating min/max quantifiers and therefore naturally fall into a higher stage of the polynomial hierarchy. Despite this,…
We introduce an extension of Dual Dynamic Programming (DDP) to solve linear dynamic programming equations. We call this extension IDDP-LP which applies to situations where some or all primal and dual subproblems to be solved along the…
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a…
Robust MDPs (RMDPs) can be used to compute policies with provable worst-case guarantees in reinforcement learning. The quality and robustness of an RMDP solution are determined by the ambiguity set---the set of plausible transition…
This work uniquely combines an affine linear decision rule known from adjustable robustness with min-max-regret robustness. By doing so, the advantages of both concepts can be obtained with an adjustable solution that is not…
We introduce StoDCuP (Stochastic Dynamic Cutting Plane), an extension of the Stochastic Dual Dynamic Programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, the algorithm builds lower…
Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…
We consider exact deterministic mixed-integer programming (MIP) reformulations of distributionally robust chance-constrained programs (DR-CCP) with random right-hand sides over Wasserstein ambiguity sets. The existing MIP formulations are…
In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true…
This article introduces a novel distributionally robust model predictive control (DRMPC) algorithm for a specific class of controlled dynamical systems where the disturbance multiplies the state and control variables. These classes of…
We introduce an extension of Dual Dynamic Programming (DDP) to solve convex nonlinear dynamic programming equations. We call Inexact DDP (IDDP) this extension which applies to situations where some or all primal and dual subproblems to be…