Discovery of new complementarity functions for NCP and SOCCP

Peng, Fei; Chen, Jein Shan; Huang, Chien Hao; Ko, Chun-Hsu

doi:10.1007/s40314-018-0660-0

Cited by 5 publications

(5 citation statements)

References 33 publications

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“…Some existing SOC complementarity functions are indeed variants of FB and NR . Recently, Ma, Chen, Huang, and Ko [41] explored the idea of "discrete generalization" to the Fischer-Burmeister function which yields the following class of functions (denoted by D−FB ):…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

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Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete‐Type Classes of SOC Complementarity Functions

Sun

Saheya

et al. 2019

Mathematical Problems in Engineering

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This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…where > 1 is a positive odd integer and (⋅) + means the projection onto K . The functions D−FB and NR are continuously differentiable SOC complementarity functions with computable Jacobian, which can be found in [41].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete‐Type Classes of SOC Complementarity Functions

Sun

Saheya

et al. 2019

Mathematical Problems in Engineering

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“…Derivative-free algorithms [4,2,3,11,14,17,20,22,24,31,33] are particularly suitable for problems where the derivatives of F are not available or are extremely expensive to compute. Next, we introduce some common penalized NCP-functions in Derivative-free algorithms.…”

mentioning

confidence: 99%

“…In this paper, we intend to unify above penalized NCP-functions and give some regular conditions for stationary points of penalized NCP-functions to be the solutions of NCPs. The main contribution is to unify and generalize some results in [4,2,3,11,14,17,20,22,24,31,33]. Based on CHS penalized NCP-function, we analyze a scaling algorithm for NCPs.…”

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confidence: 99%

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Penalized NCP-functions for nonlinear complementarity problems and a scaling algorithm

Wang

2022

JIMO

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<p style='text-indent:20px;'>In this paper, we systematically study the properties of penalized NCP-functions in derivative-free algorithms for nonlinear complementarity problems (NCPs), and give some regular conditions for stationary points of penalized NCP-functions to be solutions of NCPs. The main contribution is to unify and generalize previous results. Based on one of above penalized NCP-functions, we analyze a scaling algorithm for NCPs. The numerical results show that the scaling can greatly improve the effectiveness of the algorithm.</p>

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Numerical comparisons based on new NCP-functions

Nurhidayat

Han

2020

J. Phys.: Conf. Ser.

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We consider studying numerical comparisons based on variants of new NCP-functions denoted by ϕ k p . The nonlinear programming (NLP) can be converted to nonlinear complementarity problem (NCP) by employing the Karush-Kuhn Tucker (KKT) optimality conditions. One of the most popular ways to solve NCP is Lagrangian globalization (LG) method by transforming NCP as a system of nonsmooth (semismooth) equations. The second one is a novel method named the fictitious time integration method (FTIM). We reformulate NCP as a system of nonlinear algebraic equations (NAEs) and then construct an ordinary differential equation (ODE) by utilizing time-like functions. A group preserving scheme (GPS) is a set of ODEs which is a tool for systematically reformulating into the nonlinear dynamical system (NDS). Afterward, the NDS can be manipulated to numerical equations through activating the Lorentz group SO 0(n, 1) and its Lie algebra SO 0(n, 1). The FTIM will be operated on this numerical equation in numerical simulations for getting approximation solutions. All of the numerical experiments are carried out in performance profile theories. The comparisons of new NCP-functions by utilizing FTIM and LG method will be discussed in numerical experiments. Lastly, an accurate test of both FTIM and LG method is going to be committed by performance profile concepts as well.

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Discovery of new complementarity functions for NCP and SOCCP

Cited by 5 publications

References 33 publications

Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete‐Type Classes of SOC Complementarity Functions

Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete‐Type Classes of SOC Complementarity Functions

Penalized NCP-functions for nonlinear complementarity problems and a scaling algorithm

Numerical comparisons based on new NCP-functions

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