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An unconstrained smooth minimization reformulation of the second-order cone complementarity problem
TLDR
A popular approach to solving the nonlinear complementarity problem (NCP) is to reformulate it as the global minimization of a certain merit function over ℝn. Expand
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Analysis of nonsmooth vector-valued functions associated with second-order cones
TLDR
We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiable, continuous differentiability and (ρ-order) semismoothness. Expand
  • 108
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A family of NCP functions and a descent method for the nonlinear complementarity problem
TLDR
We propose a family of new NCP functions, which include the Fischer-Burmeister function as a special case, based on a p-norm with p being any fixed real number in the interval (1,+∞), and show several favorable properties of the proposed functions. Expand
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Two classes of merit functions for the second-order cone complementarity problem
  • Jein-Shan Chen
  • Mathematics, Computer Science
  • Math. Methods Oper. Res.
  • 7 November 2006
TLDR
We extend a class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP. Expand
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Entropy-like proximal algorithms based on a second-order homogeneous distance function for quasi-convex programming
TLDR
We consider two classes of proximal-like algorithms for minimizing a proper lower semicontinuous quasi-convex function f(x) subject to non-negative constraints $$x \geq 0$. Expand
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Recurrent neural networks for solving second-order cone programs
TLDR
This paper proposes using the neural networks to efficiently solve the second-order cone programs (SOCP). Expand
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Symmetrization of generalized natural residual function for NCP
TLDR
We symmetrize the generalized natural residual NCP-function, a natural extension of the Fischer-Burmeister function that does not possess symmetric graph, and construct not only new N CP-functions and merit functions for the nonlinear complementarity problem, but also provide parallel functions to the generalized Fischer-burmeister functions. Expand
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A one-parametric class of merit functions for the second-order cone complementarity problem
TLDR
We investigate a one-parametric class of merit functions for the second-order cone complementarity problem (SOCCP) which is closely related to the popular Fischer–Burmeister (FB) merit function and natural residual merit function. Expand
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The SC1 property of the squared norm of the SOC Fischer-Burmeister function
TLDR
We show that the gradient mapping of the squared norm of Fischer-Burmeister function is globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving nonlinear second-order cone complementarity problems via the conjugate gradient method and the Semismooth Newton's method. Expand
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A Class of Interior Proximal-Like Algorithms for Convex Second-Order Cone Programming
TLDR
We propose a class of interior proximal-like algorithms for the second- order cone program, which is to minimize a closed proper convex function subject to general second-order cone constraints. Expand
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