A merit function method for infinite-dimensional SOCCPs |
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Authors: | Yungyen Chiang Shaohua Pan Jein-Shan Chen |
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Institution: | a Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan b School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China c Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan |
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Abstract: | We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H, and then define a one-parametric class of complementarity functions Φt on H×H with the parameter t∈0,2). We show that the squared norm of Φt with t∈(0,2) is a continuously F(réchet)-differentiable merit function. By this, the second-order cone complementarity problem (SOCCP) in H can be converted into an unconstrained smooth minimization problem involving this class of merit functions, and furthermore, under the monotonicity assumption, every stationary point of this minimization problem is shown to be a solution of the SOCCP. |
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Keywords: | Hilbert space Complementarity Second-order cone Merit functions |
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