Journal ArticleDOI
Path-following methods for linear programming
TLDR
A unified treatment of algorithms is described for linear programming methods based on the central path, which is a curve along which the cost decreases, and that stays always far from the centre.Abstract:
In this paper a unified treatment of algorithms is described for linear programming methods based on the central path. This path is a curve along which the cost decreases, and that stays always far...read more
Citations
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Journal ArticleDOI
Semidefinite programming
Lieven Vandenberghe,Stephen Boyd +1 more
TL;DR: A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given.
Journal ArticleDOI
A trust region method based on interior point techniques for nonlinear programming
TL;DR: This paper focuses on the primal version of the new algorithm, an algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints, which applies sequential quadratic programming techniques to a sequence of barrier problems.
Book ChapterDOI
Disciplined Convex Programming
TL;DR: A new methodology for constructing convex optimization models called disciplined convex programming is introduced, which enforces a set of conventions upon the models constructed, in turn allowing much of the work required to analyze and solve the models to be automated.
Book
Numerical Optimization: Theoretical and Practical Aspects
TL;DR: This book is about the theoretical foundations of optimization algorithms, and also provides practical insights on how such methods should be implemented and applied, and provides adequate examples to help the reader understand the methods better and explore possible pitfalls.
Journal ArticleDOI
Optimal reactive dispatch through interior point methods
TL;DR: An implementation of an interior point method to the optimal reactive dispatch problem is described in this article, which is based on the primal-dual algorithm and the numerical results in large scale networks (1832 and 3467 bus systems) have shown that this technique can be very effective to some optimal power flow applications.
References
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Journal ArticleDOI
A new polynomial-time algorithm for linear programming
TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).
Book
Nonlinear Programming: Sequential Unconstrained Minimization Techniques
TL;DR: This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere.
Journal ArticleDOI
On the Implementation of a Primal-Dual Interior Point Method
TL;DR: A Taylor polynomial of second order is used to approximate a primal-dual trajectory and an adaptive heuristic for estimating the centering parameter is given, which treats primal and dual problems symmetrically.