arXiv subjects

Yongzheng Dai

Publications and source records attributed to Yongzheng Dai.

8 recordsLinked to original sources

arXiv2026

Warm-Startable Progressive Integrality Outer-Inner Approximation for AC Unit Commitment with Conic Formulation

The alternating-current unit commitment problem provides a realistic representation of power system operations, which is a nonconvex mixed-integer nonlinear programming problem and hence is computationally intractable. A common relaxation to the alternating-current unit commitment problem is based on the second-order cone, which results in a mixed-integer second-order cone program and remains computationally challenging. In this paper, we propose a warm-startable outer-inner approximation framework that alternatively solves a mixed-integer linear programming (MILP) as an outer approximation and a convex second-order cone programming as an inner approximation to find a (near-)optimal solution to the second-order cone-based alternating-current unit commitment problem. To improve computational efficiency, we introduce a progressive integrality strategy that gradually enforces integrality, reducing the reliance on expensive MILP solutions in early iterations. In addition, time-block Benders cuts are incorporated to strengthen the outer approximation and accelerate convergence. Computational experiments on large-scale test systems, including 200-bus and 500-bus networks, demonstrate that the proposed framework significantly improves both efficiency and robustness compared to state-of-the-art commercial solvers.

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arXiv2026

Polyhedral Outer-Approximations for MISOCP: Geometry and Cutting Planes

Mixed-integer second-order cone programs are commonly solved by polyhedral outer approximation (OA), which iteratively strengthens a linear relaxation of the conic feasible region through cutting planes. We study how such approximations can be constructed more efficiently. First, we analyze the marginal contribution of a newly generated cut relative to cuts already present in the relaxation. Using violation- and volume-based measures, we show that this contribution decreases at least as fast as linearly as the new supporting direction approaches an existing one. Motivated by this geometric analysis, we develop a cut-generation strategy that balances separation depth with angular novelty and admits closed-form constructions. Second, we introduce a progressive-integrality OA framework that proceeds from an LP relaxation through partially integral relaxations before reaching the full MILP, thereby using inexpensive early iterations to strengthen the approximation before later mixed-integer solves. Computational experiments on CBLIB instances and large-scale AC unit-commitment models demonstrate complementary benefits from the proposed cut strategy and progressive integrality, substantially reducing the computational effort of outer approximation.

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arXiv2026

Scheduling Electricity Production Units to Mitigate Severe Weather Impact: An Efficient Computational Implementation

Extreme weather events in electric power systems can cause line trips or physical damage to transmission infrastructure, potentially leading to large-scale load shedding. To mitigate this risk, we propose a framework that strategically pre-positions the commitment of generation units--particularly slow-start units--to adapt to transmission topologies that may arise following such events. The objective is to minimize load shedding under worst-case conditions. This paper makes two main contributions. First, we provide a more accurate representation of the underlying physical laws than those used in prior studies. Second, we develop a highly efficient solution algorithm that outperforms state-of-the-art, off-the-shelf solvers. The proposed framework is formulated as a two-stage robust optimization model. In the first stage, generation units are scheduled in anticipation of disruptions. In the second stage, power dispatch decisions are optimized to minimize load shedding under the worst-case transmission topology. To ensure system reliability and security, we incorporate convexified AC power flow constraints. The resulting model is a tri-level mixed-integer nonlinear optimization problem. To address its computational complexity, we design a problem-specific outer approximation algorithm embedded within a column-and-constraint generation framework. Computational results show that the proposed model and solution approach can achieve solutions within a standard optimality gap in a reasonable time for moderately large instances.

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arXiv2026

An Alternating Primal Heuristic for Nonconvex MIQCQP with Dynamic Convexification and Parallel Local Branching

We develop a novel primal heuristic for nonconvex Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQPs). The method is built around a convex approximation that is dynamically adjusted within a feasibility-pump-style alternating heuristic. Approximations are adjusted based on the structure of the MIQCQP instance. Additionally, parallelized local branching is incorporated to further refine detected solutions. This paper builds upon the second-place finalist submission in the 2025 Land-Doig MIP Computational Competition. Our results are validated with computational experiments on instances from QPLIB, finding feasible solutions for three previously unsolved cases and improving the best-known solutions for fifteen instances within five minutes of runtime.

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arXiv2025

Serial and Parallel Two-Column Probing for Mixed-Integer Programming

Probing in mixed-integer programming (MIP) is a technique of temporarily fixing variables to discover implications that are useful to branch-and-cut solvers. Such fixing is typically performed one variable at a time -- this paper develops instead a two-column probing scheme that instead fixes a pair of variables per iteration. Although the scheme involves more work per iteration compared to the one-column approach, stronger implied bounds as well as more conflicts identified may compensate. Indeed, our prototype implementation was awarded first prize at the MIP Workshop 2024 Computational Competition on novel presolving approaches. This paper presents the aforementioned (serial) prototype and additionally develops an efficient parallelization, leveraging hardware acceleration to further improve overall solve times. Compared to serial two-column probing, our parallel version sacrifices some strength per-pair probed in exchange for greatly increasing the total number of such probings; computational experiments demonstrate its promise.

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arXiv2025

Parallelized Conflict Graph Cut Generation

A conflict graph represents logical relations between binary variables, and effective use of the graph can significantly accelerate branch-and-cut solvers for mixed-integer programming (MIP). In this paper we develop efficient parallel conflict graph management: conflict detection; maximal clique generation; clique extension; and clique merging. We leverage parallel computing in order to intensify computational effort on the conflict graph, thereby generating a much larger pool of cutting planes than what can be practically achieved in serial. Computational experiments demonstrate that the expanded pool of cuts enabled by parallel computing lead to substantial reductions in total MIP solve time, especially for more challenging cases.

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arXiv2024

Tensor Completion via Integer Optimization

The main challenge with the tensor completion problem is a fundamental tension between computation power and the information-theoretic sample complexity rate. Past approaches either achieve the information-theoretic rate but lack practical algorithms to compute the corresponding solution, or have polynomial-time algorithms that require an exponentially-larger number of samples for low estimation error. This paper develops a novel tensor completion algorithm that resolves this tension by achieving both provable convergence (in numerical tolerance) in a linear number of oracle steps and the information-theoretic rate. Our approach formulates tensor completion as a convex optimization problem constrained using a gauge-based tensor norm, which is defined in a way that allows the use of integer linear optimization to solve linear separation problems over the unit-ball in this new norm. Adaptations based on this insight are incorporated into a Frank-Wolfe variant to build our algorithm. We show our algorithm scales-well using numerical experiments on tensors with up to ten million entries.

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arXiv2023

Sparsity-Exploiting Distributed Projections onto a Simplex

Projecting a vector onto a simplex is a well-studied problem that arises in a wide range of optimization problems. Numerous algorithms have been proposed for determining the projection; however, the primary focus of the literature has been on serial algorithms. We present a parallel method that decomposes the input vector and distributes it across multiple processors for local projection. Our method is especially effective when the resulting projection is highly sparse; which is the case, for instance, in large-scale problems with i.i.d. entries. Moreover, the method can be adapted to parallelize a broad range of serial algorithms from the literature. We fill in theoretical gaps in serial algorithm analysis, and develop similar results for our parallel analogues. Numerical experiments conducted on a wide range of large-scale instances, both real-world and simulated, demonstrate the practical effectiveness of the method.

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