Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2002.09743

Generalized Adaptive Partition-based Method for Two-Stage Stochastic Programs with Fixed Recourse

Cristian Ramirez-Pico·Eduardo Moreno
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a method to solve two-stage stochastic problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a discrete problem with one scenario for each element of the partition (sub-regions of the uncertainty space). Fixing first stage variables, we formulate a second stage subproblem for each element, and exploiting information from the dual of these problems, we provide conditions that the partition must satisfy to obtain the optimal solution. These conditions provide guidance on how to refine the partition, converging iteratively to the optimal solution. Results from computational experiments show how the method automatically refines the partition of the uncertainty space in the regions of interest for the problem. Our algorithm is a generalization of the adaptive partition-based method presented by Song & Luedtke (2015) for discrete distributions, extending its applicability to more general cases.

Explore related subjects

math.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Cristian Ramirez-Pico, Eduardo Moreno. 2020-03-03. Generalized Adaptive Partition-based Method for Two-Stage Stochastic Programs with Fixed Recourse. https://doi.org/10.1007/s10107-020-01609-8

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Strategic Inference in Stackelberg Games: Optimal Control for Revealing Adversary Intent

We study a continuous-time stochastic Stackelberg game in which a leader seeks to accomplish a primary objective while inferring a hidden parameter of a rational follower. The follower solves an entropy-regularized linear-quadratic tracking problem and responds to the leader's trajectory with a randomized policy. Anticipating this response, the leader designs informative controls to maximize the estimation efficiency for the follower's latent intent, through maximum likelihood estimation. Unlike prior work on discrete-time or finite-candidate inverse learning, our framework enables continuous parameter inference without prior assumptions and endogenizes the information source through the follower's strategic feedback. We derive semi-explicit solutions, prove well-posedness, and develop recurrent neural network algorithms to approximate the leader's path-dependent control. Numerical experiments demonstrate how the leader balances task performance and information gain, highlighting the practical value of our approach for adversarial strategic inference.

math.OC↗
arXiv2026

Stratification for Nonlinear Semidefinite Programming

This paper introduces a stratification framework for nonlinear semidefinite programming (NLSDP) that reveals and utilizes the geometry behind the nonsmooth KKT system. Based on the index stratification of $\mathbb{S}^n$ and its lift to the primal-dual space, a stratified variational analysis is developed. Specifically, we define the stratum-restricted regularity property, characterize it by the verifiable weak second order condition (W-SOC) and weak strict Robinson constraint qualification (W-SRCQ), and interpret the W-SRCQ geometrically via transversality, with stability along strata. The interactions of these properties across neighboring strata are further examined, leading to the conclusion that classical strong-form regularity conditions correspond to the local uniform validity of stratum-restricted counterparts. On the algorithmic side, a stratified Gauss--Newton method with normal steps and a correction mechanism is proposed for globally solving the KKT equation through a least-squares merit function. We demonstrate that the algorithm converges globally to directional stationary points. Moreover, under the second order sufficient condition (SOSC) and the strict Robinson constraint qualification (SRCQ) at an accumulation point, with a suitable correction threshold, the whole sequence converges superlinearly to this point, which is a KKT pair, and eventually identifies the active stratum. The rate is quadratic if the problem data are additionally of class $LC^2$ near the solution.

math.OC↗
arXiv2026

Convergence Rate Analysis of SOAP with Arbitrary Orthogonal Projection Matrices

In this short note, we establish, for the first time, the convergence rate of SOAP, an efficient and popular matrix-based optimizer for training deep neural networks. Our analysis extends to a more general variant of SOAP that admits arbitrary orthogonal projection matrices and requires only that these matrices be conditionally independent of the current stochastic gradient at each iteration. For example, they may be constructed from information available up to the preceding step.

math.OC↗