On Solving Convex Optimization Problems with Linear Ascending Constraints

TL;DR

This paper introduces two algorithms for convex optimization with linear ascending constraints, improving complexity for separable objectives and extending to non-separable cases, with demonstrated numerical effectiveness.

Contribution

The paper presents a dual method with finite termination and a gradient projection method for broader convex problems, advancing solution efficiency and applicability.

Findings

Dual method terminates in finite steps

Improved worst-case complexity over previous methods

Algorithms perform well in numerical tests

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. Optimization, 20 (2009), pp. 1185-1204]. 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.