Bifurcation Problems for Some Parametric Nonlinear Programs in Banach Spaces
Aubrey B. Poore · SIAM Journal on Control and Optimization · 1996
Singularities in a class of parametric nonlinear programming problems in Banach spaces are investigated using bifurcation theory. Motivated by the Fritz John first-order necessary conditions and a nonstandard normalization of the multipliers, this problem is first formulated as a system of nonlinear equations. Conditions for this system to be Fredholm are then derived, and singularities are shown to arise from a violation of one or more of the following conditions: strict complementarily, surjectivity of the Fréchet derivative of the active constraints, and a second-order condition. A branching analysis is developed for each of these singularities under a second-order nondegeneracy assumption. Examples from the calculus of variations are then used to illustrate these singularities.