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FEASIBLE DESCENT CONE METHODS FOR INEQUALITY CONSTRAINED OPTIMIZATION PROBLEMS
Author(s) -
SNYMAN J. A.,
STANDER N.
Publication year - 1996
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/(sici)1097-0207(19960430)39:8<1341::aid-nme907>3.0.co;2-j
Subject(s) - descent (aeronautics) , descent direction , mathematics , sequence (biology) , mathematical optimization , cone (formal languages) , feasible region , gradient descent , linear inequality , quadratic equation , algorithm , boundary (topology) , computer science , inequality , artificial neural network , geometry , mathematical analysis , machine learning , biology , genetics , engineering , aerospace engineering
A new Feasible Descent Cone (FDC) method for constrained optimization, previously restricted to linear objectives, is here generalized to include non‐linear objective functions as well. In the basic and exact algorithm a sequence of descent steps is taken through the interior of the feasible region along the central lines of mathematically defined descent cones, constructed at successive boundary points. Here the basic algorithm is modified to allow for a minimum to occur within the interior, along a central descent ray in the case of non‐linear objectives. A special interior procedure, with desirable mathematical properties, is adopted should the latter occur. To ensure economic implementation, the new generalized and exact algorithm, referred to as SSOPT2, is successively applied to a sequence of approximate quadratic subproblems. The overall generalized procedure that includes the successive application of SSOPT2 to the approximate subproblems, is referred to as the successive approximation version 2 algorithm (SAM2). The practical performance of SAM2 is assessed through its application to a number of small but otherwise representative test problems.