Three-term conjugate gradient method for the convex optimization problem over the fixed point set of a nonexpansive mapping |
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Authors: | Hideaki Iiduka |
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Institution: | Network Design Research Center, Kyushu Institute of Technology, 2-2-3 Uchisaiwai-cho, Chiyoda-ku, Tokyo 100-0011, Japan |
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Abstract: | Many constrained sets in problems such as signal processing and optimal control can be represented as a fixed point set of a certain nonexpansive mapping, and a number of iterative algorithms have been presented for solving a convex optimization problem over a fixed point set. This paper presents a novel gradient method with a three-term conjugate gradient direction that is used to accelerate conjugate gradient methods for solving unconstrained optimization problems. It is guaranteed that the algorithm strongly converges to the solution to the problem under the standard assumptions. Numerical comparisons with the existing gradient methods demonstrate the effectiveness and fast convergence of this algorithm. |
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Keywords: | Convex optimization problem Fixed point set Convex function Nonexpansive mapping Conjugate gradient method Three-term conjugate gradient method |
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