A graph-based decomposition method for convex quadratic optimization with indicators

Autor: Peijing Liu, Salar Fattahi, Andrés Gómez, Simge Küçükyavuz
Rok vydání: 2022
Předmět:
Zdroj: Mathematical Programming.
ISSN: 1436-4646
0025-5610
DOI: 10.1007/s10107-022-01845-0
Popis: In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix $Q$ defining the quadratic term in the objective is sparse. We use a graphical representation of the support of $Q$, and show that if this graph is a path, then we can solve the associated problem in polynomial time. This enables us to construct a compact extended formulation for the closure of the convex hull of the epigraph of the mixed-integer convex problem. Furthermore, we propose a novel decomposition method for general (sparse) $Q$, which leverages the efficient algorithm for the path case. Our computational experiments demonstrate the effectiveness of the proposed method compared to state-of-the-art mixed-integer optimization solvers.
Databáze: OpenAIRE
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