Dennis, John E., Jr.2009-06-042009-06-041991Overley, H. Kurt. "Structured secant updates for nonlinear constrained optimization." (1991) Diss., Rice University. <a href="https://hdl.handle.net/1911/16470">https://hdl.handle.net/1911/16470</a>.https://hdl.handle.net/1911/16470Two new updates are presented, the UHU update and a modified Gurwitz update, for approximating the Hessian of the Lagrangian in nonlinear constrained optimization problems. Under the standard assumptions, the new UHU algorithm is shown to converge locally at a two-step q-superlinear rate. With the additional assumption that the update can be performed at every iteration, the UHU method converges locally at a one-step q-superlinear rate. Numerical experiments are performed on some full Hessian methods including Powell's modified BFGS and Tapia's ASSA and SALSA algorithms, and on reduced Hessian methods including the two new updates, the Coleman-Fenyes update, the Nocedal-Overton method, and the two-stage Gurwitz update. These experiments show that the new updates compare favorably with existing methods.68 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.MathematicsOperations researchThesisThesis Math.Sci. 1991 Overley