Convexification of multi-period quadratic programs with indicators

• 成果类型: Article; Early Access
• 署名作者: Lee, Jisun; Gomez, Andres; Atamturk, Alper
• 署名单位: University System of Georgia; Georgia Institute of Technology; University of Southern California; University of California System; University of California Berkeley
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-026-02379-5
• 发表日期: 2026-07-22
• 关键词: mixed-integer optimization; Block-factorizable matrix; convexification; Tridiagonal inverse; Shortest path problem; second-order cone programming; strong formulations; log n); algorithm; time; optimization; inequalities; complexity; inverse; cuts

摘要

We study a multi-period mixed-integer convex quadratic optimization problem, where the state evolves dynamically as an affine function of the state and action (control) variables in each period. We begin by projecting out the state variables using linear dynamics, resulting in a mixed-integer quadratic optimization problem with a positive-definite (block-)factorizable cost matrix. Employing this expression, we construct a closed convex hull representation of the epigraph of the quadratic cost over the feasible region in an extended space. Subsequently, we establish a tight second-order cone programming formulation with O(n2) conic constraints. We further propose a polynomial-time algorithm based on a reformulation of the problem as a shortest path problem on a directed acyclic graph. To illustrate the applicability of our results across diverse domains, we present case studies in statistical learning and hybrid system control.