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 Error Bound property in mathematical programming

2019 ◽  
Vol 55 (3) ◽  
pp. 309-318
Author(s):  
D. E. Berezhnov ◽  
L. I. Minchenko
Keyword(s):  
Mathematical Programming ◽  
Large Class ◽  
Optimality Conditions ◽  
Error Bound ◽  
Numerical Optimization ◽  
Constraint Qualification ◽  
Necessary Conditions ◽  
Optimization Algorithms ◽  
Sufficient Conditions ◽  
Mathematical Programming Problems

This article is devoted to the Error Bound property (also named R-regularity) in mathematical programming problems. This property plays an important role in analyzing the convergence of numerical optimization algorithms, a topic covered by multiple publications, and at the same time it is a relatively generic constraint qualification that guarantees the satisfaction of the necessary Kuhn – Tucker optimality conditions in mathematical programming problems. In the article, new sufficient conditions for the error bound property are described, and it’s also shown that several known necessary conditions are insufficient. The sufficient conditions obtained can be used to prove the regularity of a large class of sets including sets that cannot be proven regular by other known constraints.

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.

Numerical Optimization Algorithm for Unsteady Flows of Rotor based on Web Service

2019 ◽  
pp. -1--1
Author(s):  
Jilin Zhang ◽  
Xuechao Liu ◽  
Jian Wan ◽  
Yongjian Ren ◽  
Binglin Xu ◽  
...  
Keyword(s):  
Web Service ◽  
Optimization Algorithm ◽  
Numerical Optimization ◽  
Unsteady Flows
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