半正定規劃

Abstract

在半正定規劃的問題中，我們要求一些對稱矩陣的彷射組合必須是半正定，在這樣的限制下試圖將目標線性函數最小化。這些限制未必是線性，但它們具有中凸的性質故半正定規劃是一種中凸規劃。在這篇論文中我們探討了一些半正定規劃的基本性質與基礎理論並給出證明。

In semidefinite programming problems one minimizes a linear function subject to some constraints which requires an affine combination of symmetric matrices to be positive semidefinite. The constraints may not be linear but it is convex so semidefinite programming problems are convex optimization problems. In this paper we give some basic properties and fundamental theorems with their proofs regrading semidefinite programming problems.