Optimization modeling via conic optimization

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400203
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyushu University
• Principal Investigator: Waki Hayato 九州大学, マス・フォア・インダストリ研究所, 准教授 (00567597)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: H∞制御 / 行列不等式 / 半正定値計画問題 / 不変零点 / 面的縮小法 / 混合整数非線形計画問題 / 分枝限定法

Outline of Final Research Achievements

We discuss two subjects: (i) H_infty control in control theory, and (ii) variable selection in statistics. For (i), we revealed that stable invariant zeros or invariant zeros on the imaginary axis of a given generalized plant causes the ill-conditionedness in the linear matrix inequality (abbr. LMI) of H_infty control. Moreover, we propose a reduction of LMI based on stable invariant zeros and apply it to LMI of H_infty control with SISO generalized plant. For (ii), we provide an MINLP formulation for variable selection based on optimization, and
propose a branch-and-bound algorithm for this formulation. Then we exploit linear dependence in a data matrix to improve the performance of our MINLP formulation.

Free Research Field

最適化理論