Abstract
This paper proposes a BFGS-SQP method for linearly constrained optimization where the objective function f is required only to have a Lipschitz gradient. The Karush-Kuhn-Tucker system of the problem is equivalent to a system of nonsmooth equations F(v) = 0. At every step a quasi-Newton matrix is updated if ∥F(vk)∥ satisfies a rule. This method converges globally, and the rate of convergence is superlinear when f is twice strongly differentiable at a solution of the optimization problem. No assumptions on the constraints are required. This generalizes the classical convergence theory of the BFGS method, which requires a twice continuous differentiability assumption on the objective function. Applications to stochastic programs with recourse on a CM5 parallel computer are discussed.
Original language | English |
---|---|
Pages (from-to) | 2051-2063 |
Number of pages | 13 |
Journal | SIAM Journal on Control and Optimization |
Volume | 34 |
Issue number | 6 |
DOIs | |
Publication status | Published - 1 Jan 1996 |
Externally published | Yes |
Keywords
- Convex programming
- Nonsmooth equations
- Quasi-Newton methods
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics