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A platform for research: civil engineering, architecture and urbanism
Decentralized hierarchical constrained convex optimization
Abstract This paper proposes a decentralized optimization algorithm for the triple-hierarchical constrained convex optimization problem of minimizing a sum of strongly convex functions subject to a paramonotone variational inequality constraint over an intersection of fixed point sets of nonexpansive mappings. The existing algorithms for solving this problem are centralized optimization algorithms using all the information in the problem, and these algorithms are effective, but only under certain additional restrictions. The main contribution of this paper is to present a convergence analysis of the proposed algorithm in order to show that the proposed algorithm using incremental gradients with diminishing step-size sequences converges to the solution to the problem without any additional restrictions. Another contribution of this paper is the elucidation of the practical applications of hierarchical constrained optimization in the form of network resource allocation and optimal control problems. In particular, it is shown that the proposed algorithm can be applied to decentralized network resource allocation with a triple-hierarchical structure.
Decentralized hierarchical constrained convex optimization
Abstract This paper proposes a decentralized optimization algorithm for the triple-hierarchical constrained convex optimization problem of minimizing a sum of strongly convex functions subject to a paramonotone variational inequality constraint over an intersection of fixed point sets of nonexpansive mappings. The existing algorithms for solving this problem are centralized optimization algorithms using all the information in the problem, and these algorithms are effective, but only under certain additional restrictions. The main contribution of this paper is to present a convergence analysis of the proposed algorithm in order to show that the proposed algorithm using incremental gradients with diminishing step-size sequences converges to the solution to the problem without any additional restrictions. Another contribution of this paper is the elucidation of the practical applications of hierarchical constrained optimization in the form of network resource allocation and optimal control problems. In particular, it is shown that the proposed algorithm can be applied to decentralized network resource allocation with a triple-hierarchical structure.
Decentralized hierarchical constrained convex optimization
Iiduka, Hideaki (author)
2019
Article (Journal)
English
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