Numerical Methods for Nonlinearly Constrained Optimization

Technical Report · Mon Mar 01 04:00:00 EST 1976

DOI:https://doi.org/10.2172/1453943· OSTI ID:1453943

Wright, Margart Ann Hagen ^[1]

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1. SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

A detailed description of a new feasible-point algorithm for nonlinearly constrained optimization is presented. The new method is based on the properties of the trajectory of minima obtained by varying the barrier parameter of the logarithmic barrier function. The algorithm is closely related to a nonfeasible-point method based on the trajectory of the quadratic penalty function, and this method is also described in detail. The search direction in the trajectory algorithms is determined by solving a quadratic programming sub-problem whose objective function is based on an approximation to the Lagrangian function. This sub-problem is well-posed whatever the value of the penalty or barrier parameter, unlike the determination of the search direction for penalty and barrier function methods. The step taken along the search direction is obtained by considering an appropriate reduction in the respective penalty or barrier function. For the quadratic penalty function, this step can be efficiently determined by a regular safeguarded linear search; for a barrier function, however, it is crucial to use specially designed linear searches. A description is included of penalty and barrier function methods, and of some other methods which, like the trajectory algorithms, are based on the Lagrangian function. A comprehensive set of programs has been developed, and a selection of typical numerical results is presented. A primary concern was with practical algorithms, and the need to consider methods that will converge even from a poor initial estimate of the solution. 23 figures.

• Research Organization: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: AC02-76SF00515
• OSTI ID: 1453943
• Report Number(s): SLAC-R--193; SLAC--193
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING