@techreport{NA-08/18,
  abstract = "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 computationally nonviable. This paper presents a second- derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which "guides" the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established.",
  author = "Nicholas I. M. Gould and Daniel P. Robinson",
  institution = "Oxford University Computing Laboratory",
  month = "November",
  number = "NA-08/18",
  title = "A second derivative SQP method: Theoretical issues",
  year = "2008",
}