Stochastic Programming – Optimization Online

Stochastic Augmented Lagrangian Framework with Second-Order Convergence Guarantees for Nonconvex Expectation-Constrained Optimization

Published: 2026/09/23

In this paper, we propose and analyze an augmented Lagrangian framework for solving stochastic nonconvex optimization problems with expectation-based equality constraints over a closed and convex constraint set. The framework generates a sequence of nonconvex primal subproblems, which are solved inexactly using stochastic second-order methods. We establish iteration complexity results for obtaining approximate second-order stationary … Read more

A sufficient convergence condition for generalized Benders decomposition with general dual functions

Published: 2026/09/22

Bingqian Liu

(Mixed) Integer Linear Programming, Convex and Nonsmooth Optimization, Convex Optimization, Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming finite convergence, general dual function, generalized benders decomposition, uniform local strongness

We revisit the framework of generalized Benders decomposition over a compact but non-finite master domain. We show by counterexample that strong general dual functions alone may fail to guarantee convergence. We then define a condition of uniform local strongness and prove that strong general dual functions satisfying this condition guarantee finite \(\epsilon\)-termination. Finally, we show … Read more

Data-Driven Police Staffing

Published: 2026/09/17

Applications - OR and Management Sciences, Scheduling, Stochastic Programming graph coloring, integer l-shaped method, police operations, two-stage stochastic integer programming

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

Two-stage approach for the predispatch problem with uncertain demand using splitting variables in interior-point methods

Published: 2026/09/16

Applications - Science and Engineering, Quadratic Programming, Stochastic Programming interior point methods, optimal power flow, Splitting Variables., stochastic optimization

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

Two-Stage Stochastic Optimization for Capacitated Facility Location Under Demand Uncertainty

Published: 2026/09/14

Sofiat Ajide

(Mixed) Integer Linear Programming, Facility Planning and Design, Stochastic Programming facility location, optimization under uncertainty, sensitivity analysis, stochastic programming, Two-Stage Recourse, Value of the Stochastic Solution

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

An exact algorithm for the probabilistic TSP via a new tractable convex representation of recourse

Published: 2026/09/12

(Mixed) Integer Linear Programming, Convex Optimization, Stochastic Programming Convex recourse representation, exact algorithm, mixed-integer linear programming, Probabilistic traveling salesman problem, stochastic routing

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

A Proximal Approach for Nonsmooth Composite-Constrained Optimization

Published: 2026/09/11

Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming composite optimization, improvement function, nonsmooth nonconvex optimization, proximal method

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

Non-monotone direct-search methods for deterministic and stochastic derivative-free optimization

Published: 2026/09/10

Nonlinear Optimization, Stochastic Programming derivate-free optimization, direct search, Non-monotone methods, worst-case complexity

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

Robust Out-of-Distribution Stochastic Optimization with Heterogeneous Inclusive and Exclusive Distribution Clusters

Published: 2026/09/10, Updated: 2026/09/18

Biao Han

Infinite Dimensional Optimization, Robust Optimization, Stochastic Programming Biconvex optimization, bilevel optimization, cognitive science, convex optimization, Data-Driven Robust Optimization, decision science, distributionally robust optimization (DRO), Machine learning and optimization, multiple kernel learning

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

Nonconvex stochastic zeroth-order optimization with decision-dependent distributions: from momentum tracking to coupled sampling

Published: 2026/09/06

Xiao Wang

Nonlinear Optimization, Stochastic Programming, Unconstrained Optimization

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