Soobin Choi – Optimization Online

Convexification of mixed-integer quadratic optimization via decision diagrams

Published: 2026/08/24, Updated: 2026/08/25

(Mixed) Integer Nonlinear Programming, Dynamic Programming convexification, decision diagrams, mixed-integer quadratic optimization

We study mixed-integer quadratic optimization (MIQO) problems with indicator variables. We propose a unified framework, based on decision diagrams, that serves both to solve the associated optimization problems and to construct ideal conic quadratic extended formulations of the closure of the convex hull of the underlying mixed-integer set. The construction applies to arbitrary quadratics and … Read more

Rank-one convexification for convex quadratic optimization with step function penalties

Published: 2025/04/25, Updated: 2026/08/25

(Mixed) Integer Nonlinear Programming, Data Science Applications, Semi-definite Programming convexification, Support Vector Machine

We investigate convexification in convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step function. First, we derive the convex hull for the epigraph of a quadratic function defined by a rank-one matrix. Using this rank-one convexification, we … Read more