On solving convex optimization problems with linear ascending constraints

On solving convex optimization problems with linear ascending constraints

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Article ID: iaor201526245
Volume: 9
Issue: 5
Start Page Number: 819
End Page Number: 838
Publication Date: Jun 2015
Journal: Optimization Letters
Authors:
Keywords: programming: convex, heuristics
Abstract:

In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In particular, the worst case complexity of our dual method improves over the best‐known result for this problem in Padakandla and Sundaresan (SIAM J Optim 20(3):1185–1204, 2009). We then propose a gradient projection method to solve a more general class of problems in which the objective function is not necessarily separable. Numerical experiments show that both our algorithms work well in test problems.

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