Daniel P. Robinson 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 the formulation and analysis of a new sequential quadratic programming (\SQP) method for general nonlinearly constrained optimization. The method pairs a primal-dual generalized augmented Lagrangian merit function with a \emph{flexible} line search to obtain a sequence of improving estimates of the solution. This function is a primal-dual variant of the augmented Lagrangian proposed … Read more
This paper studies the solution of two problems—bound-constrained quadratic programs and linear complementarity problems—by two-phase methods that consist of an active set prediction phase and a subspace phase. The algorithms enjoy favorable convergence properties under weaker assumptions than those assumed for other methods in the literature. The active set prediction phase employs matrix splitting iterations … Read more
We consider a class of infeasible, path-following methods for convex quadratric programming. Our methods are designed to be effective for solving both nondegerate and degenerate problems, where degeneracy is understood to mean the failure of strict complementarity at a solution. Global convergence and a polynomial bound on the number of iterations required is given. An … Read more
The solution of trust-region and regularisation subproblems which arise in unconstrained optimization is considered. Building on the pioneering work of Gay, More’ and Sorensen, methods which obtain the solution of a sequence of parametrized linear systems by factorization are used. Enhancements using high-order polynomial approximation and inverse iteration ensure that the resulting method is both … Read more
Gould and Robinson (NAR 08/18, Oxford University Computing Laboratory, 2008) gave global convergence results for a second-derivative SQP method for minimizing the exact $\ell_1$-merit function for a \emph{fixed} value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. … Read more
Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be … Read more
Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be … Read more
Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both … Read more