Large police departments usually operate by assigning regular patrol units to pre-defined regions, with backup units covering multiple regions to handle periods of high demand or replace unavailable regular units. We develop a data-driven approach to determine the optimal number and deployment of these backup units across different shifts, minimizing the expected travel time to … Read more
The stochastic predispatch optimal power flow problem aims to minimize generation costs and transmission losses subject to network constraints under demand uncertainty. We formulate it as a two-stage stochastic quadratic optimization problem with fixed recourse, in which hydroelectric generation constitutes the here-and-now decision, while thermal generation and transmission flows are recourse decisions. Using a splitting-variable … Read more
Facility location decisions are typically made before demand is fully known, yet most applied studies solve a single deterministic model using expected or nominal demand. This paper formulates and solves a capacitated facility location problem using a real academic benchmark instance, then extends it to a two-stage stochastic program in which facility-opening decisions are made … Read more
We consider the probabilistic traveling salesman problem (PTSP) in which customer presences are Bernoulli random variables, and the objective is to determine an a priori tour minimizing the expected traveling cost of the a posteriori tour obtained by skipping absent customers after customer presence is revealed. The existing literature has established that, given an a … Read more
We propose a proximal-type algorithm for nonsmooth and nonconvex optimization problems with composite constraints. The constraint is defined by the composition of a locally upper-\(C^2\) outer function with a locally Lipschitz continuous inner mapping. The method is based on an improvement function that balances objective decrease and constraint satisfaction, and on a surrogate model obtained … Read more
In derivative-free optimization (DFO), one minimizes functions for which the gradient is unavailable or expensive to compute. In many applications, objective function values and gradients are noisy due to simulations or system randomness. A class of standard direct-search methods for DFO accept a trial point when it decreases the objective function by an amount proportional … Read more
Decision scenarios far from rare in practice often place data-driven decision-making in an awkward position, where the decision maker may have access to neither the target distribution itself nor any empirical samples drawn from it, especially when decisions must be made in novel or highly uncertain environments. In response, robust out-of-distribution stochastic optimization (RooDSO) has … Read more
In this paper, we study nonconvex stochastic optimization with {decision-dependent distributions}, where the decision variable influences the underlying sampling distribution and only stochastic function-value feedback is available. We address two challenges {induced by decision-dependent distributions}: transport error in momentum-based gradient tracking and variance inflation in zeroth-order estimation. We first develop a Polyak-momentum zeroth-order method that … Read more
We develop a novel Dantzig-Wolfe (DW) decomposition algorithm for monotone two-stage stochastic mixed-integer programs (SMIPs). The key novelty in this algorithm is to relax the non-anticipativity constraints (NACs) in line with the monotonicity in the problem. We prove (i) that the relaxed restricted master problem (RMP) faster identifies dominated columns that cannot improve the RMP … Read more
We present an inexact Augmented Lagrangian algorithm for solving nonlinear, non-convex optimization problems. Unlike most recently proposed Augmented Lagrangian methods with worst-case complexity guarantees, we utilize adaptive penalty parameter updates and full dual stepsizes. We show that the method matches the best known worst-case complexity results for Augmented Lagrangian methods (up to logarithmic factors) when … Read more