arXiv subjects

Ningji Wei

Publications and source records attributed to Ningji Wei.

5 recordsLinked to original sources

arXiv2026

Scalable Finite Adaptability via Polyhedral Partition and Learning

We study finite adaptability for decision-making under uncertainty, where a small set of candidate solutions is prepared in advance and the best response is selected after uncertainty is realized. While existing methods have made significant progress on exact formulations, scalability remains a persistent challenge due to (i) the combinatorial nature of assigning decisions to uncertainty realizations, and (ii) the joint optimization of uncertainty set partition and subsequent decisions. We propose a framework that makes the partition of the uncertainty set explicit and uses polyhedral partitions as the basis for policy design. Under mild regularity conditions and for general risk measures, we show that such policies converge to the optimal fully adjustable policy as the number of regions increases. Building on this result, we develop a parametric partition framework that allows flexible policy design with tractable reformulations for both robust and stochastic finite adaptability problems. To improve scalability, we introduce an approximate-learn-parallel framework that integrates partition learning with parallel optimization while preserving solution robustness. Computational experiments on classical testbeds in both robust and stochastic settings show that the proposed method scales to larger instances and yields competitive policy performance.

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arXiv2025

Set System Approximation for Binary Integer Programs: Reformulations and Applications

Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these inequalities as primitives for set system approximation in binary integer programs (BIPs). We show that arbitrary set systems admit tight inner and outer monotone approximations, exactly corresponding to covering and elimination inequalities. Building on this, we develop a toolkit that both recovers classical structural correspondences (e.g., paths vs. cuts, spanning trees vs. cycles) and extends polyhedral tools from set covering to general BIPs, including facet conditions and lifting methods. We also propose new reformulation techniques for nonlinear and latent monotone systems, such as auxiliary-variable-free bilinear linearization, bimonotone cuts, and interval decompositions. A case study on distributionally robust network site selection illustrates the framework's flexibility and computational benefits. Overall, this unified view clarifies inner/outer approximation criteria, extends classical polyhedral analysis, and provides broadly applicable reformulation strategies for nonlinear BIPs.

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arXiv2025

GFORS: GPU-Accelerated First-Order Method with Randomized Sampling for Binary Integer Programs

We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that generates batched binary candidates. Both components are designed to run end-to-end on GPUs with minimal CPU-GPU synchronization. The framework establishes near-stationary-point guarantees for the first-order routine and probabilistic bounds on the feasibility and quality of sampled solutions, while not providing global optimality certificates. To improve sampling effectiveness, we introduce techniques such as total-unimodular reformulation, customized sampling design, and monotone relaxation. On classic benchmarks (set cover, knapsack, max cut, 3D assignment, facility location), baseline state-of-the-art exact solvers remain stronger on small-medium instances, while GFORS attains high-quality incumbents within seconds; on large instances, GFORS yields substantially shorter runtimes, with solution quality often comparable to -- or better than -- the baseline under the same time limit. These results suggest that GFORS can complement exact solvers by delivering scalable, GPU-native search when problem size and response time are the primary constraints.

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arXiv2025

A Gauge Set Framework for Flexible Robustness Design

This paper proposes a unified framework for designing robustness in optimization under uncertainty using gauge sets, convex sets that generalize distance and capture how distributions may deviate from a nominal reference. Representing robustness through a gauge set reweighting formulation brings many classical robustness paradigms under a single convex-analytic perspective. The corresponding dual problem, the upper approximator regularization model, reveals a direct connection between distributional perturbations and objective regularization via polar gauge sets. This framework decouples the design of the nominal distribution, distance metric, and reformulation method, components often entangled in classical approaches, thus enabling modular and composable robustness modeling. We further provide a gauge set algebra toolkit that supports intersection, summation, convex combination, and composition, enabling complex ambiguity structures to be assembled from simpler components. For computational tractability under continuously supported uncertainty, we introduce two general finite-dimensional reformulation methods. The functional parameterization approach guarantees any prescribed gauge-based robustness through flexible selection of function bases, while the envelope representation approach yields exact reformulations under empirical nominal distributions and is asymptotically exact for arbitrary nominal choices. A detailed case study demonstrates how the framework accommodates diverse robustness requirements while admitting multiple tractable reformulations.

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arXiv2024

Convexoid: A Minimal Theory of Conjugate Convexity

A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the minimal requirements to establish these results? This paper aims to address this inquiry through a carefully crafted system called the convexoid. We demonstrate that fundamental constructs, such as conjugate functions and subdifferentials, along with their relationships, can be derived within this minimal system. Building on this, we define the associated duality systems and develop conditions for weak and strong duality, generalizing the classic results from conjugate duality and radial duality theories. Due to its flexibility, our framework supports various approximation schemes, including approximating general functions using symmetric-conic, bilinear, radial, or piecewise constant functions, and representing general structures such as graphs, set systems, fuzzy sets, or toposes using special membership functions. The associated duality results for these systems also open new opportunities for establishing bounds on objective values and verifying structural properties.

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