A Primal-Dual Quasi-Newton Method for Constrained Optimization

Nakayama, H. & Orimo, M. (1984). A Primal-Dual Quasi-Newton Method for Constrained Optimization. IIASA Collaborative Paper. IIASA, Laxenburg, Austria: CP-84-044

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One of the most important developments in nonlinear constrained optimization in recent years has been the recursive quadratic programming (RQP) method suggested by Wilson, Han, Powell and many other researchers. It is clear that the role of the auxiliary quadratic programming problem is to calculate (implicitly) the inverse Hessian of the dual objective function. We describe the Hessian of the Lagrangian and that of the dual objective function as the primal Hessian and the dual Hessian, respectively. In this paper, a new method for constrained optimization, called the primal-dual quasi-Newton method, is proposed. The main feature of this method is that it improves (explicitly) both the primal Hessian and the dual Hessian using quasi-Newton methods. Several variants of the primal-dual quasi-Newton method are possible: the properties of these methods are described and the computational results obtained for some test problems are given.

Item Type: Monograph (IIASA Collaborative Paper)
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:55
Last Modified: 27 Aug 2021 17:12
URI: https://pure.iiasa.ac.at/2533

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