On the Convexification of a Class of Mixed-Integer Conic Sets

2025/11/01 by Du, Guxin, Chen, Rui, Wei, Linchuan
#FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2511.00452

Abstract

We investigate mixed-integer second-order conic (SOC) sets with a nonlinear right-hand side in the SOC constraint, a structure frequently arising in mixed-integer quadratically constrained programming (MIQCP). Under mild assumptions, we show that the convex hull can be exactly described by replacing the right-hand side with its concave envelope. This characterization enables strong relaxations for MIQCPs via reformulations and cutting planes. Computational experiments on distributionally robust chance-constrained knapsack variants demonstrate the efficacy of our reformulation techniques.

Citations

• Constrained Optimization of Rank-One Functions with Indicator Variables
• Explicit convex hull description of bivariate quadratic sets with indicator variables
• On the convex hull of convex quadratic optimization problems with indicators
• Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications
• Quadratic Optimization with Switching Variables: The Convex Hull for n = 2
• On the tightness of SDP relaxations of QCQPs
• Exact Semidefinite Formulations for a Class of (Random and Non-Random) Nonconvex Quadratic Programs
• Submodularity in conic quadratic mixed 0-1 optimization
• How to Convexify the Intersection of a Second Order Cone and a Nonconvex Quadratic
• Two-Term Disjunctions on the Second-Order Cone
• Intersection Cuts for Nonlinear Integer Programming: Convexification Techniques for Structured Sets
• A branch-and-cut method for 0-1 mixed convex programming

Related

• Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications
• Convex Mixed-Integer Nonlinear Programs Derived from Generalized Disjunctive Programming using Cones
• Convexification of classes of mixed-integer sets with L^\natural-convexity
• A note on quadratic constraints with indicator variables: Convex hull description and perspective relaxation
• Concave tents: a new tool for constructing concave reformulations of a large class of nonconvex optimization problems