Time-Dependent Mathematical Programs.
Final rept. 25 Jun 74-24 Jun 77,
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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The principal device and unifying theme of research summarized here is to be the homotopy principle for solving equations. To solve a given system of equations, the system is first deformed to one which is trivial and has a unique solution. Beginning with the solution to the trivial problem a route of solutions is followed as the system is deformed, perhaps with retrogression, back to the given system. The route terminates with a solution to the given problem. The principle was first stated as such in Homotopies for Computation of Fixed Points, a research report by the principle investigator which was supported earlier by ARO. Principal accomplishments under the research contract is the accomplishment of significant unification in particular, it was shown that the complementary pivot and fixed point methods are all in theory the same and that a strong link between these methods and differential topology exists. This report consists of abstracts of eight reports emanating from the research. Author
- Theoretical Mathematics