A Globally Convergent Stabilized SQP Method: Superlinear Convergence

Regularized and stabilized sequential quadratic programming (SQP) methods are two classes of methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that allows convergence to points satisfying certain second-order KKT conditions (SIAM J. Optim., 23(4):1983–2010, 2013). The method is … Read more

AN INEQUALITY-CONSTRAINED SQP METHOD FOR EIGENVALUE OPTIMIZATION

We consider a problem in eigenvalue optimization, in particular find- ing a local minimizer of the spectral abscissa – the value of a parameter that results in the smallest magnitude of the largest real part of the spectrum of a matrix system. This is an important problem for the stabilization of control sys- tems. Many … Read more

SQP Methods for Parametric Nonlinear Optimization

Sequential quadratic programming (SQP) methods are known to be effi- cient for solving a series of related nonlinear optimization problems because of desirable hot and warm start properties–a solution for one problem is a good estimate of the solution of the next. However, standard SQP solvers contain elements to enforce global convergence that can interfere … Read more

A Regularized SQP Method with Convergence to Second-Order Optimal Points

Regularized and stabilized sequential quadratic programming methods are two classes of sequential quadratic programming (SQP) methods designed to resolve the numerical and theoretical difficulties associated with ill-posed or degenerate nonlinear optimization problems. Recently, a regularized SQP method has been proposed that provides a strong connection between augmented Lagrangian methods and stabilized SQP methods. The method … Read more