Resolving degeneracy in an exact penality function technique for nonlinear bilevel optimization
- Univ. of Waterloo (Canada)
The general bilevel programming is a multilevel mathematical program consisting of two nonlinear optimization problems connected by a solution constraint: min{sub x, y} F(x, y) subject to x {element_of} X, y {element_of} R(x), where R(x) = arg min{sub y} {l_brace}f(x, y) : y {element_of} Y (x){r_brace}. We solve this difficult problem by replacing the inner problem with its Kuhn-Tucker necessary optimality conditions, creating a related single level optimization problem, which is solved using an exact {ell}{sub 1} penality function technique. The structure and nondifferentiability of the penality function made it difficult to extend existing degeneracy resolving techniques to this problem. After much work, a generalized set of necessary optimality conditions using two levels of multipliers was developed. These conditions are used constructively to find a first order descent direct at a degenerate point, or to determine that no such direction exists.
- OSTI ID:
- 35875
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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