Solving convex QPs with structured sparsity under indicator conditions

Daniel Bienstock; Tongtong Chen

Solving convex QPs with structured sparsity under indicator conditions

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arxiv 2411.11722 v1 pith:2PDP5SUE submitted 2024-11-18 math.OC cs.CCcs.DS

Daniel Bienstock , Tongtong Chen This is my paper

classification math.OCcs.CCcs.DS

keywords convexconditionsindicatorvariablesalgorithmsapproximationbinaryblocks

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We study convex optimization problems where disjoint blocks of variables are controlled by binary indicator variables that are also subject to conditions, e.g., cardinality. Several classes of important examples can be formulated in such a way that both the objective and the constraints are separable convex quadratics. We describe a family of polynomial-time approximation algorithms and negative complexity results.

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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.

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