Complexity analysis and numerical implementation of a full-Newton step interior-point algorithm for LCCO

In this paper, we present a primal-dual interior point algorithm for linearly constrained convex optimization (LCCO). The algorithm uses only full-Newton step to update iterates with an appropriate proximity measure for controlling feasible iterations near the central path during the solution proces...

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Bibliographic Details
Published in:Numerical algorithms Vol. 70; no. 2; pp. 393 - 405
Main Authors: Achache, Mohamed, Goutali, Moufida
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2015
Springer Nature B.V
Subjects:
Algebra
Algorithms
Complexity
Computer Science
Convexity
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Polynomials
Theory of Computation
Interior point methods
90C51
Linearly constrained convex optimization
Short-step primal-dual algorithms
90C25
Complexity of algorithms
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, we present a primal-dual interior point algorithm for linearly constrained convex optimization (LCCO). The algorithm uses only full-Newton step to update iterates with an appropriate proximity measure for controlling feasible iterations near the central path during the solution process. The favorable polynomial complexity bound for the algorithm with short-step method is obtained, namely O ( n log n 𝜖 ) which is as good as the linear and convex quadratic optimization analogue. Numerical results are reported to show the efficiency of the algorithm.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-014-9955-4