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
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
We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math Prog 122(1):155–196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism, … Read more
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
A new method for solving sequences of quadratic programs (QPs) is presented. For each new QP in the sequence, the method utilizes hot-starts that employ information computed by an active-set QP solver during the solution of the first QP. This avoids the computation and factorization of the full matrices for all but the first problem … Read more
We present a sequential quadratic optimization (SQO) algorithm for nonlinear constrained optimization. The method attains all of the strong global and fast local convergence guarantees of classical SQO methods, but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances. A two-phase strategy, carefully constructed … Read more
We present a filter linesearch method for solving general nonlinear and nonconvex optimization problems. The method is of the filter variety, but uses a robust (always feasible) subproblem based on an exact penalty function to compute a search direction. This contrasts traditional filter methods that use a (separate) restoration phase designed to reduce infeasibility until … Read more
We propose a sequential quadratic optimization method for solving nonlinear optimization problems with equality and inequality constraints. The novel feature of the algorithm is that, during each iteration, the primal-dual search direction is allowed to be an inexact solution of a given quadratic optimization subproblem. We present a set of generic, loose conditions that the … Read more
Sequential quadratic programming (SQP) methods are a popular class of methods for nonlinearly constrained optimization. They are particularly effective for solving a sequence of related problems, such as those arising in mixed-integer nonlinear programming and the optimization of functions subject to differential equation constraints. Recently, there has been considerable interest in the formulation of \emph{stabilized} … Read more
We present a new tree-search algorithm for solving mixed-integer nonlinear programs (MINLPs). Rather than relying on computationally expensive nonlinear solves at every node of the branch-and-bound tree, our algorithm solves a quadratic approximation at every node. We show that the resulting algorithm retains global convergence properties for convex MINLPs, and we present numerical results on … Read more