UC Research Repository Collection:http://hdl.handle.net/10092/6112015-07-29T06:48:41Z2015-07-29T06:48:41ZAccelerations for global optimization methods that use second derivative informationBaritompa, William P.Cutler, Adelehttp://hdl.handle.net/10092/107102015-07-28T12:30:22Z1993-01-01T00:00:00ZTitle: Accelerations for global optimization methods that use second derivative information
Authors: Baritompa, William P.; Cutler, Adele
Abstract: Two new improvements for the algorithm of Breiman & Cutler are presented. Better envelopes can be built up using positive definite quadratic forms. Better utilization of first and second derivative information is attained by combining both global aspects of curvature and local aspects nearthe global optimum. The basis of the results is the geometric viewpoint developed by the first author and can be applied to a number of covering type methods. Improvements in convergence rates are demonstrated empirically on standard test functions.1993-01-01T00:00:00ZA projected Lagrangian algorithm for semi-infinite programmingCoope, Ian D.Watson, G. A.http://hdl.handle.net/10092/107092015-07-28T12:30:22Z1983-01-01T00:00:00ZTitle: A projected Lagrangian algorithm for semi-infinite programming
Authors: Coope, Ian D.; Watson, G. A.
Abstract: A globally convergent algorithm is presented for the solution of a wide class of semi-infinite programming problems. The method is based on the solution of a sequence of equality constrained quadratic programming problems, and usually has a second order convergence rate. Numerical results illustrating the effectiveness of the method are given.1983-01-01T00:00:00ZUniform approximation from Tchebycheff systemsBrookes, Richard Gordonhttp://hdl.handle.net/10092/107052015-07-28T12:30:21Z1987-01-01T00:00:00ZTitle: Uniform approximation from Tchebycheff systems
Authors: Brookes, Richard Gordon
Abstract: This report is concerned with the study of best uniform approximation
to f E C[a,b) from the linear space generated by some finite subset
U == {uo,u1, ... ,u} of C[a,b).
n
p* E span U such that
By a best uniform approximation we mean
max{jf(x) ~p*(x) j: x E [a,b]} = min{max{jf(x) -p(x) I x E [a,b]}
: p E span u}.
We explore, firstly, the case U = {l,x, ... ,xn}. It will be shown in
Section 4 that in this situation each f E C[a,b) has a unique best approximation
and for this best approximation there is a strong characterisation
theorem. It is then natural to ask whether these results are true for a
more general U = {u 0 ,u 1 , ••• ,u } .
n
If a strong type of linear independence
known as the Haar condition is imposed on U then this will indeed turn out
1.
to be the case. We will attempt to develop this condition using an approach
more intuitively obvious than those found in many standard texts.
When the Haar condition is not satisfied the problem rapidly becomes
complicated and it appears that much work remains to be done in this area.
A theorem concerning a particularly simple situation is given in Section 8.1987-01-01T00:00:00ZThe existence and local behaviour of the quadratic function approximationBrookes, Richard GordonMcInnes, A.W.http://hdl.handle.net/10092/107032015-07-28T12:30:21Z1988-01-01T00:00:00ZTitle: The existence and local behaviour of the quadratic function approximation
Authors: Brookes, Richard Gordon; McInnes, A.W.
Abstract: This paper analyses the local behaviour of the quadratic function approximation to a function which has a given power series expansion about the origin. It is shown that the quadratic Hermite-Padé form always defines a quadratic function and that this function is analytic in a neighbourhood of the origin. This result holds even if the origin is a critical point of the function (i.e. the discriminant has a zero at the origin). If the discriminant has multiple zeros the order of the approximation will be degraded but only to a limited extent.1988-01-01T00:00:00Z