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.

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.

A Class of Augumented Lagrangian Function for Nonlinear Programming

2011 ◽  
Vol 271-273 ◽  
pp. 1955-1960
Author(s):  
Mei Xia Li
Keyword(s):  
Nonlinear Programming ◽  
Programming Problem ◽  
Inequality Constraints ◽  
Unconstrained Minimization ◽  
Lagrangian Function ◽  
Point Of View ◽  
Theoretical Point ◽  
Non Linear Programming ◽  
Global Minimizers ◽  
Equality And Inequality Constraints

In this paper, we discuss an exact augumented Lagrangian functions for the non- linear programming problem with both equality and inequality constraints, which is the gen- eration of the augmented Lagrangian function in corresponding reference only for inequality constraints nonlinear programming problem. Under suitable hypotheses, we give the relation- ship between the local and global unconstrained minimizers of the augumented Lagrangian function and the local and global minimizers of the original constrained problem. From the theoretical point of view, the optimality solution of the nonlinear programming with both equality and inequality constraints and the values of the corresponding Lagrangian multipli- ers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augumented Lagrangian function presented in this paper.

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.

Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models

1989 ◽  
Vol 5 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Frank A. Wolak
Keyword(s):  
Econometric Model ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Test Statistic ◽  
Model Framework ◽  
Global Inequality ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Class Of Estimators

This paper considers a general nonlinear econometric model framework that contains a large class of estimators defined as solutions to optimization problems. For this framework we derive several asymptotically equivalent forms of a test statistic for the local (in a way made precise in the paper) multivariate nonlinear inequality constraints test H: h(β) ≥ 0 versus K: β ∈ RK. We extend these results to consider local hypotheses tests of the form H: h1(β) ≥ 0 and h2(β) = 0 versus K: β ∈ RK. For each test we derive the asymptotic distribution for any size test as a weighted sum of χ2-distributions. We contrast local as opposed to global inequality constraints testing and give conditions on the model and constraints when each is possible. This paper also extends the well-known duality results in testing multivariate equality constraints to the case of nonlinear multivariate inequality constraints and combinations of nonlinear inequality and equality constraints.

scholarly journals Second-Order Multiplier Iteration Based on a Class of Nonlinear Lagrangians

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yong-Hong Ren
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Second Order ◽  
Constrained Optimization Problems ◽  
Lipschitz Continuous ◽  
First Order ◽  
Nonlinear Lagrangians ◽  
Nonlinear Lagrangian ◽  
Nonlinear Lagrangian Algorithm

Nonlinear Lagrangian algorithm plays an important role in solving constrained optimization problems. It is known that, under appropriate conditions, the sequence generated by the first-order multiplier iteration converges superlinearly. This paper aims at analyzing the second-order multiplier iteration based on a class of nonlinear Lagrangians for solving nonlinear programming problems with inequality constraints. It is suggested that the sequence generated by the second-order multiplier iteration converges superlinearly with order at least two if in addition the Hessians of functions involved in problem are Lipschitz continuous.

Optimization of Constrained Dynamic Systems Using the Sequential Unconstrained Minimization Technique

1972 ◽  
Vol 94 (4) ◽  
pp. 319-322 ◽  
Author(s):  
B. N. Murali ◽  
L. R. Ebbesen ◽  
H. R. Sebesta
Keyword(s):  
Nonlinear Programming ◽  
Dynamic Systems ◽  
Optimization Problem ◽  
State Constraints ◽  
Unconstrained Minimization ◽  
Terminal State ◽  
Analysis Tool ◽  
Minimization Technique ◽  
Algebraic Optimization ◽  
Nonlinear Programming Method

The development of a computer program for the optimization of dynamic systems subject to parameter and terminal state constraints is presented in this paper. The problem is handled by converting it to an equivalent algebraic optimization problem. The resulting problem is then solved by a modified version (D YS UMT) of the nonlinear programming method S UMT (Sequential Unconstrained Minimization Technique). The available program provides an efficient and convenient analysis tool to aid engineers in the modeling and designing of dynamic systems.

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