Computational Optimization and Applications
Second-order negative-curvature methods for box-constrained and general constrained optimization
Computational Optimization and Applications
A reduced Hessian SQP method for inequality constrained optimization
Computational Optimization and Applications
Manifold identification in dual averaging for regularized stochastic online learning
The Journal of Machine Learning Research
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We show that the quadratic growth condition and the Mangasarian--Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an $L_\infty$ exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.