The Lack of Positive Definiteness in the Hessian in Constrained Optimization
Abstract
The use of the DFP or the BFGS secant updates requires the Hessian at the solution to be positive-definite. The second order sufficiency conditions insure the positive definiteness only in a sub-space of R(exp n). Conditions are given so the author can safely update with either update. The author proposes a new class of algorithms that generate a sequence converging 2-step q-superlinearly. He also proposes two specific algorithms. The first one converges q-superlinearly if the Hessian is positive-definite in R(exp n), and it converges 2-step q-superlinearly if the Hessian is positive-definite only in a subspace. The second one generates a sequence converging 1-step q-superlinearly. While the former costs one extra gradient evaluation, the latter costs one extra gradient evaluation and one extra function evaluation on the constraints.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1983
- Accession Number
- ADA453915
Entities
People
- Rodrigo Fontecilla
Organizations
- Rice University