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A Survey of the S-Lemma
TLDR
A unified analysis of the S-lemma is given by providing three different proofs for the theory and revealing hidden connections with various areas of mathematics, to prove some new duality results and present applications from control theory, error estimation, and computational geometry. Expand
On implementing a primal-dual interior-point method for conic quadratic optimization
TLDR
The main features of the implementation are it is based on a homogeneous and self-dual model, it handles rotated quadratic cones directly, it employs a Mehrotra type predictor-corrector extension and sparse linear algebra to improve the computational efficiency and it exploits fixed variables which naturally occurs in many conic Quadratic optimization problems. Expand
Self-regularity - a new paradigm for primal-dual interior-point algorithms
An apparatus and method for continuously detecting oxygen in a carrier gas stream. The apparatus employs a sensor film comprising a fluorescent material emitting from 3000 - 8000 A, dissolved in aExpand
Theory and algorithms for linear optimization - an interior point approach
TLDR
This chapter discusses duality Theory for Linear Optimization, a Polynomial Algorithm for the Skew-Symmetric Model, and Parametric and Sensitivity Analysis, as well as implementing Interior Point Methods. Expand
Self-regular functions and new search directions for linear and semidefinite optimization
Abstract.In this paper, we introduce the notion of a self-regular function. Such a function is strongly convex and smooth coercive on its domain, the positive real axis. We show that any suchExpand
On maximization of quadratic form over intersection of ellipsoids with common center
TLDR
It is shown that this bound is sharp in order, as far as the dependence on m is concerned, and that a~feasible solution x to (P) with x^TAx\ge \frac{{\Opt(\hbox{{\rm SDP}})}}{{2\ln(2m^2)}} \eqno{(*)}$$ can be found efficiently. Expand
Interior Point Methods for Nonlinear Optimization
TLDR
After more than a decade of turbulent research, the IPM community reached a good understanding of the basics of IPMs and several books were published that summarize and explore different aspects of IPM's. Expand
Interior Point Methods for Linear Optimization
List of figures.- List of tables.- Preface.- Acknowledgements.- Introduction.- I. Introdcution: Theory and Complexity.- Duality Theory for Linear Optimization.- A Polynomial Algorithm for theExpand
Sensitivity analysis in linear programming: just be careful!
In this paper we review the topic of sensitivity analysis in linear programming. We describe the problems that may occur when using standard software and advocate a framework for performing completeExpand
The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming
In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of theExpand
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