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• W2892433564 abstract "Let <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>Q</mml:mi></mml:mrow></mml:math> be closed convex subsets of real Hilbert spaces <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>, respectively, and let <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mi>g</mml:mi><mml:mo>:</mml:mo><mml:mi>C</mml:mi><mml:mo>→</mml:mo><mml:mi mathvariant=double-struck>R</mml:mi></mml:math> be a strictly real-valued convex function such that the gradient <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mo>∇</mml:mo><mml:mi>g</mml:mi></mml:math> is an <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mrow><mml:mn mathvariant=normal>1</mml:mn></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:mrow></mml:math>-ism with a constant <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>L</mml:mi><mml:mo>></mml:mo><mml:mn mathvariant=normal>0</mml:mn></mml:math>. In this paper, we introduce an iterative scheme using the gradient projection method, based on Mann’s type approximation scheme for solving the constrained convex minimization problem (CCMP), that is, to find a minimizer <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mi>q</mml:mi><mml:mo>∈</mml:mo><mml:mi>C</mml:mi></mml:math> of the function <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math> over set <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M11><mml:mrow><mml:mi>C</mml:mi></mml:mrow></mml:math>. As an application, it has been shown that the problem (CCMP) reduces to the split feasibility problem (SFP) which is to find <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M12><mml:mi>q</mml:mi><mml:mo>∈</mml:mo><mml:mi>C</mml:mi></mml:math> such that <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M13><mml:mi>A</mml:mi><mml:mi>q</mml:mi><mml:mo>∈</mml:mo><mml:mi>Q</mml:mi></mml:math> where <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M14><mml:mi>A</mml:mi><mml:mo>:</mml:mo><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>1</mml:mn></mml:mrow></mml:msub><mml:mo>→</mml:mo><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant=normal>2</mml:mn></mml:mrow></mml:msub></mml:math> is a linear bounded operator. We suggest and analyze this iterative scheme under some appropriate conditions imposed on the parameters such that another strong convergence theorems for the CCMP and the SFP are obtained. The results presented in this paper improve and extend the main results of Tian and Zhang (2017) and many others. The data availability for the proposed SFP is shown and the example of this problem is also shown through numerical results." @default.
• W2892433564 created "2018-10-05" @default.
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• W2892433564 date "2018-10-01" @default.
• W2892433564 modified "2023-09-27" @default.
• W2892433564 title "On Solving of Constrained Convex Minimize Problem Using Gradient Projection Method" @default.
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• W2892433564 doi "https://doi.org/10.1155/2018/1580837" @default.
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