Parametric nonlinear programming problems under the relaxed constant rank condition. (English) Zbl 1229.90216
Let \(f (x,y)\) be a continuously differentiable function on \(\mathbb R^n \times\mathbb R^m\).
The authors present their work on minimizing \(f(x,y)\) over \(y \in\mathbb R^m\) subject to a finite number of constraints of the form \(h_i(x,y) < 0\) and \(h_j(x,y) = 0 \).
Generally researchers impose regularity conditions on the restraints to solve such nonlinear programming problems. Here, the authors explore a relaxed version of the constant rank condition on the error bound property, the directional differentiability of the optimal value function, and the necessity and sufficiency second order optimal condition.
The authors present their work on minimizing \(f(x,y)\) over \(y \in\mathbb R^m\) subject to a finite number of constraints of the form \(h_i(x,y) < 0\) and \(h_j(x,y) = 0 \).
Generally researchers impose regularity conditions on the restraints to solve such nonlinear programming problems. Here, the authors explore a relaxed version of the constant rank condition on the error bound property, the directional differentiability of the optimal value function, and the necessity and sufficiency second order optimal condition.
Reviewer: Daniel Wulbert (La Jolla)
MSC:
90C31 | Sensitivity, stability, parametric optimization |
41A50 | Best approximation, Chebyshev systems |
49K40 | Sensitivity, stability, well-posedness |