Saddle-Point Criteria in an η-Approximation Method for Nonlinear Mathematical Programming Problems Involving Invex Functions

2007 ◽  
Vol 132 (1) ◽  
pp. 71-87 ◽  
Author(s):  
T. Antczak
Keyword(s):  
Mathematical Programming ◽  
Saddle Point ◽  
Approximation Method ◽  
Invex Functions ◽  
Nonlinear Mathematical Programming ◽  
Mathematical Programming Problems

A Boundary Tracking Optimization Algorithm for Constrained Nonlinear Problems

1978 ◽  
Vol 100 (2) ◽  
pp. 292-296 ◽  
Author(s):  
J. Y. Moradi ◽  
M. Pappas
Keyword(s):  
Mathematical Programming ◽  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Nonlinear Problems ◽  
Nonlinear Constraints ◽  
Comparison Study ◽  
Boundary Tracking ◽  
Nonlinear Mathematical Programming ◽  
Mathematical Programming Problems ◽  
Tracking Strategy

A new procedure for numerical optimization of constrained nonlinear problems is described. The method makes use of an efficient “Boundary Tracking” strategy to move on the constraint surfaces. In a comparison study it was found to be an effective method for treating nonlinear mathematical programming problems particularly those with difficult nonlinear constraints.

scholarly journals Lagrange duality and saddle point optimality conditions for semi-infinite mathematical programming problems with equilibrium constraints

2019 ◽  
Vol 29 (4) ◽  
pp. 433-448
Author(s):  
Kunwar Singh ◽  
J.K. Maurya ◽  
S.K. Mishra
Keyword(s):  
Mathematical Programming ◽  
Saddle Point ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Mathematical Programming Problem ◽  
Dual Model ◽  
Equilibrium Constraints ◽  
Convexity Assumptions ◽  
Mathematical Programming Problems

In this paper, we consider a special class of optimization problems which contains infinitely many inequality constraints and finitely many complementarity constraints known as the semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC). We propose Lagrange type dual model for the SIMPEC and obtain their duality results using convexity assumptions. Further, we discuss the saddle point optimality conditions for the SIMPEC. Some examples are given to illustrate the obtained results.

scholarly journals Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem

2019 ◽  
Vol 10 ◽  
pp. A10
Author(s):  
Mansur Hassan ◽  
Adam Baharum
Keyword(s):  
Penalty Function ◽  
Optimization Problem ◽  
Duality Gap ◽  
Penalty Function Method ◽  
Constrained Optimization Problem ◽  
Zero Duality Gap ◽  
Invex Functions ◽  
Lagrangian Dual ◽  
Nonlinear Mathematical Programming ◽  
Mathematical Programming Problems

In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem has been used to derived KKT multiplier based on the imposed additional hypotheses on the constraint function g. A zero-duality gap between an optimization problem constituted by invex functions with respect to the same function η and their Lagrangian dual problems has also been established. The examples have been provided to illustrate and proved the result for the broader class of convex functions, termed invex functions.

Nonlinear Integer and Discrete Programming in Mechanical Design Optimization

1990 ◽  
Vol 112 (2) ◽  
pp. 223-229 ◽  
Author(s):  
E. Sandgren
Keyword(s):  
Mathematical Programming ◽  
Mechanical Design ◽  
General Purpose ◽  
Design Problems ◽  
Design Constraints ◽  
Design Variables ◽  
Nonlinear Mathematical Programming ◽  
Discrete Programming ◽  
Mathematical Programming Problems ◽  
Quadratic Programming Method

A general purpose algorithm for the solution of nonlinear mathematical programming problems containing integer, discrete, zero-one, and continuous design variables is described. The algorithm implements a branch and bound procedure in conjunction with either an exterior penalty function or a quadratic programming method. Variable bounds are handled independently from the design constraints which removes the necessity to reformulate the problem at each branching node. Examples are presented to demonstrate the utility of the algorithm for solving design problems.

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