scholarly journals Enhanced Fritz John stationarity, new constraint qualifications and local error bound for mathematical programs with vanishing constraints

2019 ◽  
Vol 472 (1) ◽  
pp. 1042-1077
Author(s):  
Abeka Khare ◽  
Triloki Nath
Keyword(s):  
Error Bound ◽  
Constraint Qualifications ◽  
Local Error ◽  
Local Error Bound ◽  
Mathematical Programs ◽  
Vanishing Constraints

scholarly journals A New Modified Efficient Levenberg–Marquardt Method for Solving Systems of Nonlinear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhenxiang Wu ◽  
Tong Zhou ◽  
Lei Li ◽  
Liang Chen ◽  
Yanfang Ma
Keyword(s):  
Error Bound ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Systems Of Nonlinear Equations ◽  
Local Error ◽  
Local Error Bound ◽  
Marquardt Method ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Local Error Bound Condition

For systems of nonlinear equations, a modified efficient Levenberg–Marquardt method with new LM parameters was developed by Amini et al. (2018). The convergence of the method was proved under the local error bound condition. In order to enhance this method, using nonmonotone technique, we propose a new Levenberg–Marquardt parameter in this paper. The convergence of the new Levenberg–Marquardt method is shown to be at least superlinear, and numerical experiments show that the new Levenberg–Marquardt algorithm can solve systems of nonlinear equations effectively.

scholarly journals On an exact penality result and new constraint qualifications for mathematical programs with vanishing constraints

2019 ◽  
Vol 29 (3) ◽  
pp. 309-324
Author(s):  
Triloki Nath ◽  
Abeka Khare
Keyword(s):  
Penalty Function ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Mathematical Programs ◽  
Vanishing Constraints ◽  
Abadie Constraint Qualification

In this paper, we considered the mathematical programs with vanishing constraints or MPVC. We proved that an MPVC-tailored penalty function, introduced in [5], is still exact under a very weak and new constraint qualification. Most importantly, this constraint qualification is shown to be strictly stronger than MPVC-Abadie constraint qualification.

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