Homotopy methods, systems of polynominal equations, and the Kuhn-Tucker conditions
Conference
·
OSTI ID:36020
Our capability to solve systems of nonlinear equations has been greatly enhanced by homotopy methods developed during the last 25 years. General systems of nonlinear equations are difficult to analyses but systems of polynomial equations represent a more manageable environment to work in. If one restricts oneself to optimization problems with objective functions and constraints being polynomials in n variables, then the Kuhn-Tucker conditions lead to a system of polynomial equations. The dominating terms of systems of polynomial equations are important for homotopy methods. In general the dominating terms for systems are not unique and a number of choices can be made. These choices affect the number of homotopy-invariant solutions one obtains. Comparisons with algebraic methods, especially with regard to computational complexity, will also briefly be discussed.
- OSTI ID:
- 36020
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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