On solving convex optimization problems with linear ascending constraints

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.