二階錐特徵值互補問題與二階錐二次特徵值互補問題的解

Abstract

本篇論文中，我們研究兩類與二階錐有關的最優化問題，包含二階錐特徵值互補問題及二階錐二次特徵值互補問題。此外，我們將這些問題換成其他架構，並在這些架構上尋找相關的演算法去解決問題。In this thesis, we study the solvabilities of two optimization problems associated with second-order cone, including eigenvalue complementarity problem associated with second order cone (SOCEiCP), and quadratic eigenvalue complementarity problem associated with second order cone (SOCQEiCP). Furthermore, we reformulate these problems and provide some algorithms for solving them.