Theory of functional connections applied to quadratic and nonlinear programming under equality constraints

2021 ◽  
pp. 113912
Author(s):  
Tina Mai ◽  
Daniele Mortari
Keyword(s):  
Nonlinear Programming ◽  
Equality Constraints ◽  
Functional Connections

A Modification of Feasible Direction Optimization Method for Handling Equality Constraints

1988 ◽  
Author(s):  
Yong Chen ◽  
Bailin Li
Keyword(s):  
Nonlinear Programming ◽  
Efficient Algorithm ◽  
Optimization Method ◽  
Equality Constraints ◽  
Feasible Region ◽  
Feasible Direction ◽  
Feasible Direction Method ◽  
Traditional Algorithm ◽  
Inequality Type ◽  
Nonlinear Equality

Abstract The Feasible Direction Method of Zoutendijk has proven to be one of the efficient algorithm currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of having equality type constraints, there does not exist nonzero direction close to the feasible region, the traditional algorithm can not work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tangent of the equality constraints at some angle which makes the move toward the interior of the feasible region.

A Modification of Feasible Direction Optimization Method for Handling Equality Constraints

1989 ◽  
Vol 111 (3) ◽  
pp. 442-445
Author(s):  
Yong Chen ◽  
Bailin Li
Keyword(s):  
Nonlinear Programming ◽  
Optimization Method ◽  
Direction Finding ◽  
Equality Constraints ◽  
Feasible Region ◽  
Feasible Direction ◽  
Feasible Direction Method ◽  
Traditional Algorithm ◽  
Inequality Type ◽  
Nonlinear Equality

The Feasible Direction Method of Zoutendijk has proven to be one of the most efficient algorithms currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of equality type constraints, there exists no nonzero direction close to the feasible region, the traditional algorithm cannot work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tangent of the equality constraints at some angle which makes the move toward the interior of the feasible region.

scholarly journals Applications of implicit parametrizations

2021 ◽  
Vol 66 (1) ◽  
pp. 5-15
Author(s):  
Dan Tiba
Keyword(s):  
Optimal Control ◽  
Nonlinear Programming ◽  
Shape Optimization ◽  
Optimality Conditions ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Equality Constraints ◽  
Control Problems ◽  
Global Type ◽  
New Algorithms

We review several applications of the implicit parametrization theorem in optimization. In nonlinear programming, we discuss both new forms, with less multipliers, of the known optimality conditions, and new algorithms of global type. For optimal control problems, we analyze the case of mixed equality constraints and indicate an algorithm, while in shape optimization problems the emphasis is on the new penalization approach.

Modification of Nonlinear Equality Constraints in Nonlinear Problems

1974 ◽  
Vol 96 (1) ◽  
pp. 138-144
Author(s):  
R. J. Polo ◽  
V. A. Sposito ◽  
T. T. Lee
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Nonlinear Problems ◽  
Unconstrained Minimization ◽  
Equality Constraints ◽  
Feasible Region ◽  
Mathematical Methods ◽  
Minimization Technique ◽  
Nonlinear Equality

This paper presents a technique for solving nonlinear programming problems with nonconvex feasible regions. The procedure expands the feasible region by replacing nonlinear equality constraints by appropriate inequality constraints. The expansion is used to solve two structural optimization problems using the sequential unconstrained-minimization technique of Fiacco and McCormick. The solutions are compared with solutions obtained by classical mathematical methods.

Extensions of SUMT for Nonlinear Programming: Equality Constraints and Extrapolation

1966 ◽  
Vol 12 (11) ◽  
pp. 816-828 ◽  
Author(s):  
Anthony V. Fiacco ◽  
Garth P. McCormick
Keyword(s):  
Nonlinear Programming ◽  
Equality Constraints
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