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Real-time solution of quadratic optimization problems with banded matrices and indicator variables

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arxiv 2405.03051 v1 pith:TDQPQ2ZI submitted 2024-05-05 math.OC

Andres Gomez , Shaoning Han , Leonardo Lozano This is my paper · ORCID
classification math.OC
keywords problemsbandeddecisiondiagramsvariablesconstructindicatormatrices
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We consider mixed-integer quadratic optimization problems with banded matrices and indicator variables. These problems arise pervasively in statistical inference problems with time-series data, where the banded matrix captures the temporal relationship of the underlying process. In particular, the problem studied arises in monitoring problems, where the decision-maker wants to detect changes or anomalies. We propose to solve these problems using decision diagrams. In particular we show how to exploit the temporal dependencies to construct diagrams with size polynomial in the number of decision variables. We also describe how to construct the convex hull of the set under study from the decision diagrams, and how to deploy the method online to solve the problems in milliseconds via a shortest path algorithm.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Coordinate Optimality Reformulation for Mixed-Integer Convex Programs with Indicators

    math.OC 2026-08 conditional novelty 7.0 of 10

    A reformulation that injects coordinate-optimality conditions into indicator MIPs sharply cuts branch-and-bound work and yields polynomial tree bounds in several structured cases.

  2. Convexification of Multi-period Quadratic Programs with Indicators

    math.OC 2024-12 conditional novelty 7.0 of 10

    Multi-period MIQPs with linear dynamics and indicators have projected cost matrices whose inverses are block-tridiagonal; the paper exploits this to give an exact O(n^2)-constraint SOCP formulation and a polynomial sh...

  3. Efficient Primal Heuristics for Mixed Binary Quadratic Programs Using Suboptimal Rounding Guidance

    math.OC 2025-01 conditional novelty 5.0 of 10

    Using a time-limited suboptimal relaxation to guide variable fixing beats using an optimal relaxation in RENS and Undercover on several MBQP benchmarks and a wind farm layout problem.

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