A generalized projection-based scheme for solving convex constrained optimization problems

Aviv Gibali (), Karl-Heinz Küfer (), Daniel Reem () and Philipp Süss ()
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Aviv Gibali: ORT Braude College
Karl-Heinz Küfer: Fraunhofer - ITWM
Daniel Reem: Technion - Israel Institute of Technology
Philipp Süss: Fraunhofer - ITWM

Computational Optimization and Applications, 2018, vol. 70, issue 3, No 4, 737-762

Abstract: Abstract In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning.

Keywords: Projection methods; Feasibility problems; Superiorization; Subgradient; Iterative methods; 65K10; 65K15; 90C25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10589-018-9991-4

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