A Unified Outline of Nonlinear Programming Algorithms

1985 ◽  
Vol 107 (4) ◽  
pp. 449-453 ◽  
Author(s):  
K. Schittkowski
Keyword(s):  
Nonlinear Programming ◽  
Sequential Quadratic Programming ◽  
Gradient Methods ◽  
Reduced Gradient ◽  
Numerical Performance ◽  
Constrained Nonlinear Programming ◽  
Generalized Reduced Gradient ◽  
Performance Results ◽  
Programming Algorithms ◽  
Reduced Gradient Methods

The four most successful approaches for solving the constrained nonlinear programming problem are the penalty, multiplier, sequential quadratic programming, and generalized reduced gradient methods. A general algorithmic frame will be presented, which realizes any of these methods only by specifying a search direction for the variables, a multiplier estimate, and some penalty parameters in each iteration. This approach allows one to illustrate common mathematical features and, on the other hand, serves to explain the different numerical performance results we observe in practice.

scholarly journals A comparative study on optimization methods for the constrained nonlinear programming problems

2005 ◽  
Vol 2005 (2) ◽  
pp. 165-173 ◽  
Author(s):  
Ozgur Yeniay
Keyword(s):  
Nonlinear Programming ◽  
Comparative Study ◽  
Sequential Quadratic Programming ◽  
Gradient Methods ◽  
Optimization Methods ◽  
Test Problems ◽  
Reduced Gradient ◽  
Constrained Nonlinear Programming ◽  
Generalized Reduced Gradient ◽  
Reduced Gradient Methods

Constrained nonlinear programming problems often arise in many engineering applications. The most well-known optimization methods for solving these problems are sequential quadratic programming methods and generalized reduced gradient methods. This study compares the performance of these methods with the genetic algorithms which gained popularity in recent years due to advantages in speed and robustness. We present a comparative study that is performed on fifteen test problems selected from the literature.

On the Global Convergence of Nonlinear Programming Algorithms

1985 ◽  
Vol 107 (4) ◽  
pp. 454-458 ◽  
Author(s):  
K. Schittkowski
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Initial Point ◽  
Convergence Result ◽  
Gradient Algorithms ◽  
Reduced Gradient ◽  
Numerical Performance ◽  
Generalized Reduced Gradient ◽  
Nonlinear Programming Methods ◽  
Programming Algorithms

In a previous paper a unified outline of some of the most successful nonlinear programming methods was presented by the author, i.e. of penalty, multiplier, sequential quadratic programming, and generalized reduced gradient algorithms, to illustrate their common mathematical features and to explain the different numerical performance observed in practice. By defining a general algorithmic frame for all these approaches, a global convergence result can be achieved in the sense that starting from an arbitrary initial point, a stationary solution will be approximated.

On the Identification of Hysteresis in Inelastic Systems

2001 ◽  
Author(s):  
Fai Ma
Keyword(s):  
Kalman Filter ◽  
Gradient Methods ◽  
Design Tool ◽  
Control Parameters ◽  
Internal Constraints ◽  
Inelastic Structures ◽  
Curve Fit ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Reduced Gradient Methods

Abstract The generalized model of differential hysteresis contains thirteen control parameters with which it can curve-fit practically any hysteretic trace. Three identification algorithms are developed to estimate the control parameters of hysteresis for different classes of inelastic structures. These algorithms are based upon the simplex, extended Kalman filter, and generalized reduced gradient methods. Novel techniques such as global search and internal constraints are incorporated to facilitate convergence and stability. Effectiveness of the devised algorithms is demonstrated through simulations of two inelastic systems with both pinching and degradation characteristics in their hysteretic traces. Due to very modest computing requirements, these identification algorithms may become acceptable as a design tool for mapping the hysteretic traces of inelastic structures.

Development of a Hybrid SQP-GRG Algorithm for Constrained Nonlinear Programming

1988 ◽  
Vol 110 (3) ◽  
pp. 308-315 ◽  
Author(s):  
A. Parkinson ◽  
M. Wilson
Keyword(s):  
Nonlinear Programming ◽  
Sequential Quadratic Programming ◽  
Hybrid Algorithm ◽  
Line Search ◽  
Programming Algorithm ◽  
Test Problems ◽  
Design Problems ◽  
Engineering Design Problems ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust, efficient, and feasible at intermediate iterations. Based on the strengths of the generalized reduced gradient (GRG) and sequential quadratic programming (SQP) algorithms, a hybrid SQP-GRG algorithm is developed. The hybrid algorithm uses the SQP search direction and a modified GRG line search. The resulting SQP-GRG algorithm is shown to be robust, feasible at intermediate iterations, and comparable in efficiency to Powell’s SQP algorithm on 26 test problems.

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