



LEADER 
04203nmm a2200289 u 4500 
001 
EB000660908 
003 
EBX01000000000000000513990 
005 
00000000000000.0 
007 
cr 
008 
140122  eng 
020 


a 9783642463297

100 
1 

a Oettli, W.
e [editor]

245 
0 
0 
a Optimization and Operations Research
h Elektronische Ressource
b Proceedings of a Conference Held at Oberwolfach, July 27–August 2, 1975
c edited by W. Oettli, K. Ritter

250 


a 1st ed. 1976

260 


a Berlin, Heidelberg
b Springer Berlin Heidelberg
c 1976, 1976

300 


a IV, 318 p. 8 illus
b online resource

505 
0 

a Reduction and Decomposition of Modulo Optimization Problems  Optimization of Elastic Structures by Mathematical Programming Techniques  On Closed Sets Having a Least Element  On the Convergence of the Variable Metric Method with Numerical Derivatives and the Effect of Noise in the Function Evaluation  Parallel Path Strategy. Theory and Numerical Illustrations  On Minimization under Linear Equality Constraints  On Constrained ShortestRoute Problems  BangBang Solution of a Control Problem for the Heat Equation  Generalized StirlingNewton Methods  On a Method for Computing Pseudoinverses  Charakterisierung lokaler ParetoOptima  On the Exact Evaluation of Finite Activity Networks with Stochastic Durations of Activities  Approximation of a Parabolic Boundary Control Problem by the Line Method  Regularisation of Optimization Problems and Operator Equations  Some Extensions of Linearly Constrained Nonlinear Programming  Boundary Control of the HigherDimensional Wave Equation  Nondifferentiable Optimisation. Subgradient and ? — Subgradient Methods  Approximations to Stochastic Optimization Problems  Models in Resource Allocation — Trees of Queues  Dual Methods in Convex Control Problems  A Subgradient Algorithm for Solving Kconvex Inequalities  Computation of BangBangControls and Lower Bounds for a Parabolic BoundaryValue Control Problem  Numerical Solution of Systems of Nonlinear Inequalities  Lower Bounds and Inclusion Balls for the Solution of Locally Uniformly Convex Optimization Problems  Über Vektormaximierung und Analyse der Gewichtung von Subzielen  Preference Optimality  Decomposition Procedures for Convex Programs

653 


a Operations research

653 


a Operations Research and Decision Theory

700 
1 

a Ritter, K.
e [editor]

041 
0 
7 
a eng
2 ISO 6392

989 


b SBA
a Springer Book Archives 2004

490 
0 

a Lecture Notes in Economics and Mathematical Systems

028 
5 
0 
a 10.1007/9783642463297

856 
4 
0 
u https://doi.org/10.1007/9783642463297?nosfx=y
x Verlag
3 Volltext

082 
0 

a 658.403

520 


a The variable metric algorithm is widely recognised as one of the most efficient ways of solving the following problem: Locate x* a local minimum point n ( 1) of f(x) x E R Considerable attention has been given to the study of the convergence prop ties of this algorithm especially for the case where analytic expressions are avai ble for the derivatives g. = af/ax. i 1 ••• n • (2) ~ ~ In particular we shall mention the results of Wolfe (1969) and Powell (1972), (1975). Wolfe established general conditions under which a descent algorithm will converge to a stationary point and Powell showed that two particular very efficient algorithms that cannot be shown to satisfy \,olfe's conditions do in fact converge to the minimum of convex functions under certain conditions. These results will be st ed more completely in Section 2. In most practical problems analytic expressions for the gradient vector g (Equ. 2) are not available and numerical derivatives are subject to truncation error. In Section 3 we shall consider the effects of these errors on Wolfe's convergent prop ties and will discuss possible modifications of the algorithms to make them reliable in these circumstances. The effects of rounding error are considered in Section 4, whilst in Section 5 these thoughts are extended to include the case of online fu tion minimisation where each function evaluation is subject to random noise
