Gradient minimax techniques for system modelling

Some recently proposed gradient methods for minimax or near minimax approximation are applied to producing optimal second-order and third-order models of a high-order system. The Fletcher-Powell method, a more recent method by Fletcher and o. method by Jacobson and Oksman are employed with least pth approximation, using large values of p, as proposed by Bandler and Charalambous and critically compared with the grazer search technique of minimax approximation by Bandler et al. The solutions obtained are shown to satisfy the necessary conditions for a minimax optimum.     

General programmes for least pth and near minimax approximation

User-oriented computer programmes in FORTRAN IV for discrete least pth approximation with a single specified function, and more generalized discrete least pth approximation with various specifications, which may also be used for non-linear programming, are presented. Values of p up to 10" can be used successfully in conjunction with efficient gradient minimization algorithms such as the Fletcher-Powell method and a method due to Fletcher. It has been demonstrated how efficiently extremely near minimax results can be achieved on a discrete sot of sample points using this approach and the programmes written verify this. The programmes may be applied to a wide variety of design problems with a wide range of specifications. They are suitable for electrical network and system design and such problems as filter design.     

THE VALUTON: AN AUTOMATION MODEL OF A SOCIOLOGICAL THEORY OF VALUE GENESIS

Abstract

Theories of value are legion, few axe satisfactory, however. Scarcity as source of value is too relativistic and also unable to explain negative evaluation of scarce objects. Labor as a basis of value cannot take account of observed variations of the value of goods. The present approach is an attempt to see value as the result of two sociological processes: proliferation and status association. The first process determines the value of a commodity by its information content, the other by a perceptional process, the halo-effect. The value of a commodity is hence the result of its history, a string of inputs. They lend themselves to be represented in form of an automaton. A prototype of such an automaton is presented, the valuton. A critical assessment concludes the article.     

Non-linear minimax optimization as a sequence of least pth optimization with finite values of p

Following developments in non-linear least pth optimization by the authors it is possible to derive two new methods of non-linear minimax optimization. Unlike the Polya algorithm in which a sequence of least pth optimizations as p→∞ is taken our methods do not require the value of p to tend to infinity. Instead we construct a sequence of least pth optimization problems with a finite value of p. It is shown that this sequence will converge to a minimax solution. Two interesting minimax problems were constructed which illustrate some of the theoretical ideas. Further numerical evidence is presented on the modelling of a fourth-order system by a second-order model with values of p varying between 2 and 10 000.     

Automated minimax system modeling†

This paper investigates the- feasibility of automated design of lower-order models for high-order systems where the order of the model can be increased efficiently according to desired performance criteria. The modelling can be done for a variety of objectives with or without constraints, so that a realistic on-line or off-line design can be achieved to satisfy a set of arbitrary transient and steady-state response specifications. Suitable examples are chosen to illustrate the modelling procedure.     

Non-linear programming using least pth optimization with extrapolation†

We present a general approach for solving minimax and non-linear programming problems through a sequence of least pth approximations with extrapolation. Several numerical examples illustrate the effectiveness of the present approach. A comparison with the woll-known SUMT method of Fiaeco and McCormick is made under the same conditions and employing Fletcher's quasi.Newton programme.     

DISOPT—A general programme for continuous and discrete non-linear programming problems†

An integrated computer programme in Fortran IV for continuous or discrete non linear programming problems is presented. Several recent techniques and algorithms for non-linear programming have been adapted and new ideas have been introduced. They include the minimax and exterior-point approaches to non-linear programming, least pth optimization and the Dakin tree-search algorithm. The user may optionally choose the combination of techniques and algorithms best suited to his problems. Since many practical design problems can be easily formulated as non-linear programming problems, the programme, called DISOPT, enjoys a very wide range of applications such as continuous and discrete tolerance assignments, digital filter design, circuit design, system modelling and approximation problems. Numerical results for a number of functions and circuit tolerance optimization problems are presented in this paper to demonstrate the performance of DISOPT.     

Light-Oxidized Flavor Development and Vitamin A Degradation in Chocolate Milk

Samples of several chocolate milk formulations were exposed to light to determine if the components masked and/or prevented light-oxidized flavors or prevented photodegradation of vitamin A. Chocolate flavor added either before or after light exposure masked light-oxidized flavor (p<0.05). Neither carrageenan nor chocolate color prevented development of light-oxidized flavor. Vitamin A degradation was reduced by the addition of carrageenan alone or in combination with chocolate dairy powder (chocolate flavor and color), chocolate color or chocolate flavor (p<0.05).