On necessary extremum conditions for finite-dimensional problems with inequality constraints

2006 ◽  
Vol 46 (11) ◽  
pp. 1860-1871
Author(s):  
D. Yu. Karamzin
Keyword(s):  
Inequality Constraints ◽  
Finite Dimensional ◽  
Necessary Extremum Conditions ◽  
Extremum Conditions

scholarly journals A Fritz John type sufficient optimality theorem in complex space

1974 ◽  
Vol 11 (2) ◽  
pp. 219-224 ◽  
Author(s):  
T.R. Gulati
Keyword(s):  
Nonlinear Programming ◽  
Complex Space ◽  
Inequality Constraints ◽  
Polyhedral Cones ◽  
Finite Dimensional

A Fritz John type sufficient optimality theorem is proved for nonlinear programming problems in finite dimensional complex space over polyhedral cones, which may include equality as well as inequality constraints.

scholarly journals A new semismooth Newton method for solving finite-dimensional quasi-variational inequalities

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shui-Lian Xie ◽  
Zhe Sun ◽  
Hong-Ru Xu
Keyword(s):  
Variational Inequalities ◽  
Newton Method ◽  
Interior Point Method ◽  
Inequality Constraints ◽  
Semismooth Newton Method ◽  
Finite Dimensional ◽  
Math Program ◽  
Semismooth Newton ◽  
Equality And Inequality Constraints ◽  
Quasi Variational Inequality

AbstractIn this paper, we consider the numerical method for solving finite-dimensional quasi-variational inequalities with both equality and inequality constraints. Firstly, we present a semismooth equation reformulation to the KKT system of a finite-dimensional quasi-variational inequality. Then we propose a semismooth Newton method to solve the equations and establish its global convergence. Finally, we report some numerical results to show the efficiency of the proposed method. Our method can obtain the solution to some problems that cannot be solved by the method proposed in (Facchinei et al. in Comput. Optim. Appl. 62:85–109, 2015). Besides, our method outperforms than the interior point method proposed in (Facchinei et al. in Math. Program. 144:369–412, 2014).

Analysis of 2-D Impedance Cloaking Problem Based on Boundary Element Method

2014 ◽  
Vol 635-637 ◽  
pp. 3-6
Author(s):  
Gennady V. Alekseev ◽  
Andrei Baydin ◽  
Olga Larkina
Keyword(s):  
Boundary Element Method ◽  
Control Problem ◽  
Boundary Element ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Optimality System ◽  
Homogenous Medium ◽  
Necessary Extremum Conditions ◽  
Extremum Conditions ◽  
Element Method

Control problems are considered for a two-dimensional model describing wave scattering in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The solvability of the original scattering problem for 2-D Helmholtz equation and of the control problem is proved. Optimality system dгescribing the necessary extremum conditions are derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

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