Ken Kobayashi – Optimization Online

A Branch-and-Cut Algorithm for Solving Mixed-integer Semidefinite Optimization Problems

Published: 2018/09/08, Updated: 2019/06/24

(Mixed) Integer Nonlinear Programming, Global Optimization, Semi-definite Programming branch-and-cut algorithm, cutting planes, mixed-integer programming, semidefinite programming

This paper is concerned with a cutting-plane algorithm for solving mixed-integer semidefinite optimization (MISDO) problems. In this algorithm, the positive semidefinite constraint is relaxed, and the resultant mixed-integer linear optimization problem is repeatedly solved with valid inequalities for the relaxed constraint. We prove convergence properties of the algorithm. Moreover, to speed up the computation, we … Read more

Mixed Integer Quadratic Optimization Formulations for Eliminating Multicollinearity Based on Variance Inflation Factor

Published: 2016/09/29, Updated: 2016/12/02

Applications - Science and Engineering, Integer Programming, Statistics integer programming, multicollinearity, multiple linear regression, statistics, subset selection, variance inflation factor

The variance inflation factor, VIF, is the most frequently used indicator for detecting multicollinearity in multiple linear regression models. This paper proposes two mixed integer quadratic optimization formulations for selecting the best subset of explanatory variables under upper-bound constraints on VIF of selected variables. Computational results illustrate the effectiveness of our optimization formulations based on … Read more

Best subset selection for eliminating multicollinearity

Published: 2016/07/26