Premium
Line search methods for extended penalty function environments
Author(s) -
Davis Caleb S.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620150607
Subject(s) - mathematics , penalty method , linear programming , mathematical optimization , quadratic equation , hyperbolic function , function (biology) , curve fitting , minification , cubic function , mathematical analysis , geometry , statistics , evolutionary biology , biology
Univariate minimization is considered for constrained optimization with the Kavlie‐Moe extended interior penalty. An algorithm is derived using a linear‐plus‐hyperbolic fit suggested by R. L. Fox for interior penalties. A linear extension to the linear‐plus‐hyperbolic permits rapid convergence with extended interior alties. However, constraint deletion and approximation of remaining constraints before each minimization also characterize the environment. These and other complexities impede accurate fitting of larger intervals. Thus, following Murray, a mixed strategy is adopted with function comparison reductions of interval size to supplement curve fitting. Analysis shows how quadratic and cubic fit searches break down under certain limiting conditions of interior, extended and exterior penalties. A quadratic‐extended linear curve derived for exterior penalties and the linear‐plus‐hyperbolic similarly fail on extended interior penalties. Examples of constrained optimization with extended interior penalties were run on the Stanford IBM 370/168 computer. A stiffened two‐panel box provides eight optimization variables with many constraints on demensions and against failure. The extended linear‐plus‐hyperbolic surpasses cubic and linear‐plus hyperbolic fitting, especially when the Fiacco‐McCormick multiplier for the penalty becomes small. The value of feedback from curve fitting to decide function comparison use is also illustrated.