Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2606.24318

A multi-objective perspective on block-structured integer programs with one soft coupling constraint

Mark Lyngesen·Kathrin Klamroth·Britta Efkes·Sune Lauth Gadegaard
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper presents a multi-objective perspective on block-structured integer programs featuring a single soft coupling constraint. By interpreting the coupling constraint as a second objective, we transform the coupled single-objective problem into an additively-separable bi-objective optimization problem. To avoid the expensive computation of the full Pareto front, we introduce an algorithm, which uses a binary search to isolate a region of interest around the soft constraint limit. This algorithm provides provable bounds on the single-objective optimum. We further enhance this algorithm, by exploiting the block-structure, using a novel $λ$-lookup mechanism to skip repeated sub-problem calculations. Finally, for scenarios requiring all non-dominated solutions within the region of interest, we propose a new approach, that works its way from the middle of the region of interest outwards. This algorithm shows quick convergence in terms of representation. Computational studies demonstrate that our methods dramatically reduce integer programming calls, thereby outperforming traditional dichotomic search. For large instances the method works as a strong heuristic providing bounds on the gap to an optimal solution, providing trade-off information in addition to the solution.

Explore related subjects

math.OC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Mark Lyngesen, Kathrin Klamroth, Britta Efkes, Sune Lauth Gadegaard. 2026-06-23. A multi-objective perspective on block-structured integer programs with one soft coupling constraint. https://arxiv.org/abs/2606.24318

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

KEEP EXPLORING

Related papers

arXiv2026

A unified analysis on the speedup of accelerated gradient methods: An inertial dynamics approach

Nesterov's Accelerated Gradient Method is one of the most popular first order optimization algorithms. When applied to $L$-smooth, $μ$-strongly convex functions, it converges at a rate of $\mathcal{O}\left(\left(1-\sqrt{\fracμ{L}}\right)^{k}\right)$. The more recent {\it Triple Momentum Method} and the {\it Information Theoretic Exact Method} enjoy an improved rate of $\mathcal{O}\left(\left(1-2\sqrt{\fracμ{L}}\right)^{k}\right)$. Their analysis relies on {\it integral quadratic constraints} and {\it performance estimation techniques}, respectively. In this work, we provide a dynamic explanation for this {\it factor 2 speedup} based on the subtle relationships between the coefficients of an inertial system with Hessian-driven damping. The standard explicit discretization of this second order ordinary differential equation produces intuitive variants of Nesterov's method with sped-up convergence rates. The proof strategy allows us to extend the analysis beyond the strongly convex setting to account for convex functions with quadratic growth or the Polyak-Łojasiewicz inequality. Under uniqueness of the minimizer, we establish a factor $\sqrt{2}$ speedup with respect to the state of the art. With no assumption on the set of minimizers, the new convergence rate (asymptotically) matches that of Gradient Descent, a fact that was previously unknown.

math.OC↗
arXiv2026

Distributed AC Optimal Power Flow: A Scalable Solution for Large-Scale Problems

This paper introduces a novel distributed optimization framework for large-scale AC Optimal Power Flow (OPF) problems, offering both theoretical convergence guarantees and rapid convergence in practice. By integrating smoothing techniques and the Schur complement, the proposed approach addresses the scalability challenges and reduces communication overhead in distributed AC OPF. Additionally, optimal network decomposition enables efficient parallel processing under the single program multiple data (SPMD) paradigm. Extensive simulations on large-scale benchmarks across various operating scenarios indicate that the proposed framework outperforms the state-of-the-art centralized solver IPOPT on modest hardware. This paves the way for more scalable and efficient distributed optimization in future power system applications.

math.OC↗
arXiv2026

Learning-Based Surrogate Method for Stochastic Optimization under Decision-Dependent Uncertainty with Adaptive Random Designs

We study stochastic programs in which the latent decision-dependent uncertainty is described via a nonparametric regression model. The major challenge is that, without convexity assumptions on either the cost function or the regression model, the resulting objective is both nonconvex and nonsmooth, and its first-order information is unavailable due to the unknown decision-dependent distribution. To address this issue, we construct a learning-based surrogate model that integrates simulation and statistical learning by embedding Jacobian estimates of the regression function, which are updated iteratively and interactively during the optimization procedure. We develop an adaptive random design that concentrates design points around the current iterate for Jacobian estimation and we show that the mean squared error of Jacobian estimates achieves a dimension-independent convergence rate. Building on this, we propose the learning-based stochastic prox-linear (L-SPL) algorithm with adaptive random design and establish its nonasymptotic convergence rates under various parameter settings. Numerical results demonstrate that L-SPL algorithm significantly improves sample efficiency and achieves substantially lower objective values compared to the state-of-the-art methods. More broadly, our method implies that the statistical design in an iterative learning-based optimization algorithm can be novelly tailored to the local information of the optimization procedure to sharpen estimates and enhance the convergence performance and sample efficiency of the resulting algorithm.

math.OC↗