Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
A generalized second-order derivative in nonsmooth optimization
SIAM Journal on Control and Optimization
Calmness and exact penalization
SIAM Journal on Control and Optimization
An exact penalization viewpoint of constrained optimization
SIAM Journal on Control and Optimization
Error bounds in mathematical programming
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Function
Mathematics of Operations Research
A Unified Augmented Lagrangian Approach to Duality and Exact Penalization
Mathematics of Operations Research
Optimality Conditions via Exact Penalty Functions
SIAM Journal on Optimization
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In this paper, by assuming that a non-Lipschitz penalty function is exact, new conditions for the existence of Lagrange multipliers are established for an inequality and equality-constrained continuously differentiable optimization problem. This is done by virtue of a first-order necessary optimality condition of the penalty problem, which is obtained by estimating Dini upper-directional derivatives of the penalty function in terms of Taylor expansions, and a Farkas lemma. Relations among the obtained results and some well-known constraint qualifications are discussed.