文档介绍：A Tutorial on Convex Optimization II: Duality and Interior Point Methods
Haitham Hindi
Palo Alto Research Center (PARC), Palo Alto, California 94304
email: hhindi@
Abstract— In recent years, convex optimization has e a and concepts. For detailed examples and applications, the
computational tool of central importance in engineering, thanks reader is refered to [8], [2], [6], [5], [7], [10], [12], [17],
to its ability to solve very large, practical engineering problems [9], [25], [16], [31], and the references therein.
reliably and efficiently. The goal of this tutorial is to continue
the overview of modern convex optimization from where our We now briefly outline the paper. There are two main
ACC2004 Tutorial on Convex Optimization left off, to cover sections after this one. Section II is on duality, where we
important topics that were omitted there due to lack of space summarize the key ideas the general theory, illustrating
and time, and highlight the intimate connections between them. the four main practical applications of duality with simple
The topics of duality and interior point algorithms will be our examples. Section III is on interior point algorithms, where
focus, along with simple examples. The material in this tutorial
is excerpted from the recent book on convex optimization, by the focus is on barrier methods, which can be implemented
Boyd and Vandenberghe, who have made available a large easily using only a few key ponents, and yet
amount of free course material and freely available software. are highly effective both in theory and in practice. All of the
These can be downloaded and used immediately by the reader theory we cover can be readily extended to general conic
both for self-study and to solve real problems. programs, such as second order cone programs (SOCP) and
semidefinite programs (SDP); see [8] for details.
I. INTRODUCTION
Notation Our notation is standard [8]. For example, we will
The objectives are to continue