Discreteness and Continuity in Infinite-dimensional Optimization

2015 Fiscal Year Final Research Report

• Project/Area Number: 24654030
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Ito Satoshi 統計数理研究所, 数理・推論研究系, 教授 (50232442)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 凸最適化 / 測度空間 / 確率測度 / 無限計画 / 半無限計画 / モーメント問題 / 通信路容量 / 相互情報量

Outline of Final Research Achievements

Most, if not all, optimization problems in infinite dimension can be regarded as those of some measure. A measure generally has an absolutely continuous component and a discrete component with respect to the Lebesgue measure. We often observe that many optimization problems in measure spaces have a discrete optimal solution. A question then arises: in what conditions does a solution to a given class of optimization problem become discrete or absolutely continuous? The purpose of this research is to give an answer to such a question.

Free Research Field

数理最適化