complementarity function
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2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Wenli Liu ◽  
Xiaoni Chi ◽  
Qili Yang ◽  
Ranran Cui

In this paper, a weighted second-order cone (SOC) complementarity function and its smoothing function are presented. Then, we derive the computable formula for the Jacobian of the smoothing function and show its Jacobian consistency. Also, we estimate the distance between the subgradient of the weighted SOC complementarity function and the gradient of its smoothing function. These results will be critical to achieve the rapid convergence of smoothing methods for weighted SOC complementarity problems.



2021 ◽  
Vol 146 ◽  
pp. 107021 ◽  
Author(s):  
Ziyun Kan ◽  
Fei Li ◽  
Haijun Peng ◽  
Biaosong Chen ◽  
XueGuan Song




Optimization ◽  
2018 ◽  
Vol 68 (1) ◽  
pp. 65-79 ◽  
Author(s):  
Roger Behling ◽  
Andreas Fischer ◽  
Klaus Schönefeld ◽  
Nico Strasdat


2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Liang Fang ◽  
Jingyong Tang ◽  
Yunhong Hu

AbstractIn this paper, nonlinear complementarity problem with P



2010 ◽  
Vol 37-38 ◽  
pp. 1153-1156
Author(s):  
Meng Zhang ◽  
Hong Ming Yang ◽  
De Lun Yang

Based on different bidding decisions with heterogeneous expectations of market participants, a dynamic model of electricity market considering power network constraints is proposed. This model is represented by a discrete difference equations embedded with the optimization problem of market clearing. By using the nonlinear complementarity function, the complex dynamic behaviors of electricity market are simulated and analyzed. The Nash equilibrium and its stability, the periodic and even chaotic dynamic behaviors beyond the stability region of Nash equilibrium are investigated.



2009 ◽  
Vol 49 (3) ◽  
pp. 457-491 ◽  
Author(s):  
Shaohua Pan ◽  
Jein-Shan Chen ◽  
Sangho Kum ◽  
Yongdo Lim


2009 ◽  
Vol 26 (02) ◽  
pp. 199-233 ◽  
Author(s):  
LINGCHEN KONG ◽  
LEVENT TUNÇEL ◽  
NAIHUA XIU

The implicit Lagrangian was first proposed by Mangasarian and Solodov as a smooth merit function for the nonnegative orthant complementarity problem. It has attracted much attention in the past ten years because of its utility in reformulating complementarity problems as unconstrained minimization problems. In this paper, exploiting the Jordan-algebraic structure, we extend it to the vector-valued implicit Lagrangian for symmetric cone complementary problem (SCCP), and show that it is a continuously differentiable complementarity function for SCCP and whose Jacobian is strongly semismooth. As an application, we develop the real-valued implicit Lagrangian and the corresponding smooth merit function for SCCP, and give a necessary and sufficient condition for the stationary point of the merit function to be a solution of SCCP. Finally, we show that this merit function can provide a global error bound for SCCP with the uniform Cartesian P-property.



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