Algorithms for separable convex optimization with linear ascending constraints

The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a separable convex function over the bases of a polymatroid w...

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Bibliographic Details
Published in:Sadhana (Bangalore) Vol. 43; no. 9; pp. 1 - 18
Main Authors: Akhil, P T, Sundaresan, Rajesh
Format: Journal Article
Language:English
Published: New Delhi Springer India 01.09.2018
Springer Nature B.V
Subjects:
Algorithms
Computational geometry
Convexity
Engineering
Optimization
Resource allocation
linear constraints
ascending constraints
OR in telecommunications
polymatroid
Convex programming
ISSN:0256-2499, 0973-7677
Online Access:Get full text
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Summary:The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a separable convex function over the bases of a polymatroid with a certain structure. The paper generalizes a prior algorithm to a wider class of separable convex objective functions that need not be smooth or strictly convex. The paper also summarizes the state-of-the-art algorithms that solve this optimization problem. When the objective function is a so-called d - separable function, a simpler linear time algorithm solves the problem.
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ISSN:0256-2499
0973-7677
DOI:10.1007/s12046-018-0890-2