Projected gradient algorithms for optimization over order simplices

A primal-dual algorithm is proposed for computing the distance from a point to an order simplex. An advantage of the algorithm is that, for any initial active set, it can adjust the active set to improve both primal and dual feasibility until the optimal active set is found. We verify that the algor...

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Bibliographic Details
Published in:Optimization methods & software Vol. 29; no. 5; pp. 1090 - 1117
Main Authors: Hu, Yi-Qing, Hao, Chun-Lin, Dai, Yu-Hong
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.09.2014
Taylor & Francis Ltd
Subjects:
Algorithms
constrained optimization
Optimization
order simplex
primal and dual feasibility
projected gradient
ISSN:1055-6788, 1029-4937
Online Access:Get full text
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Summary:A primal-dual algorithm is proposed for computing the distance from a point to an order simplex. An advantage of the algorithm is that, for any initial active set, it can adjust the active set to improve both primal and dual feasibility until the optimal active set is found. We verify that the algorithm takes only O(n) elementary arithmetic operations, where n is the problem dimension. Numerical results demonstrate the efficiency of the primal-dual algorithm compared with the primal feasible algorithm and the dual feasible algorithm. The primal-dual algorithm proves very useful in projected gradient algorithms applied to general order simplex constrained problems since a series of projection subproblems are requested there and the primal-dual algorithm makes warm starts possible.
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ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2014.911872