Search results for "Descent direction"
showing 3 items of 3 documents
On the methods of nonsmooth optimization
2005
In this paper we shall give a short derivation of the most promising methods in nonsmooth optimization, namely bundle methods. We introduce the basic bundle idea due to Lemarechal and several modifications by Kiwiel, Schramm and Zowe. To the end we shall give some numerical results comparing the efficience of these methods. As test problems we have used well-known test problems from litterature and in addition we shall give some contributions to nonsmooth optimal control problems.
A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
2006
Our goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L^1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existe…
A New Min-Max Optimisation Approach for Fast Learning Convergence of Feed-Forward Neural Networks
1993
One of the most critical aspect for a wide use of neural networks to real world problems is related to the learning process which is known to be computational expensive and time consuming.