Successive inexact Quadratic Programming for Nonlinear Optimization Problems (Large-Scale, Sqp, Qp) [electronic resource]

1984

1 online resource (101 p.)

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Source: Dissertation Abstracts International, Volume: 46-05, Section: B, page: 1667.

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Sequential quadratic programming (SQP) methods are iterative procedures for solving constrained nonlinear optimization problems. At each stage a quadratic programming subproblem has to be solved. SQP methods are attractive because they converge rapidly from any sufficiently good initial estimate of a solution. However, solving the quadratic subproblems at each stage can be expensive, particularly, if the number of unknowns is large. Furthermore, it may not be justified when the iterate is far from a solution. Therefore we consider a family of successive inexact quadratic programming (SIQP) methods that solve the subproblems only approximately. We derive conditions for local and superlinear convergence in terms of the relative error incurred in the subproblems. These conditions do not assume that the set of active constraints remains constant in a neighborhood of a solution. We then show how the error can be bounded by measurable quantities. This leads to practical termination criteria for truncating iterative algorithms applied to the quadratic subproblems. In quadratic programming based methods, the main computational effort is in solving the quadratic subproblems. Therefore, we study efficient algorithms for very large box-constrained quadratic problems and propose some new convergent methods that permit the addition and deletion of many constraints each time a search direction is calculated. We also discuss alternative applications of the SIQP framework.

Books / Online / Dissertations & Theses

July 13, 2011

Thesis (Ph.D.)--Yale University, 1984.

Yale University.