NDLI: Central Swaths : A Generalization of the Central Path

Content Provider	Springer Nature Link
Author	Renegar, James
Copyright Year	2013
Abstract	We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the “derivative cones” of a “hyperbolicity cone”, the derivatives being direct and mathematically appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other.We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path.
Ending Page	454
Page Count	50
Starting Page	405
File Format	PDF
ISSN	16153375
e-ISSN	16153383
Journal	Foundations of Computational Mathematics
Issue Number	3
Volume Number	13
Language	English
Publisher	Springer-Verlag
Publisher Date	2013-03-30
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Semidefinite programming Economics general Linear programming Symmetry properties of polytopes Linear and Multilinear Algebras, Matrix Theory Convex programming Conic programming Hyperbolicity cone Hyperbolic polynomial Convex optimization Numerical Analysis Computer Science Convex functions and convex programs Applications of Mathematics Math Applications in Computer Science Hyperbolic programming Central path
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Theory and Mathematics Computational Mathematics

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