Acceleration of the leastpth algorithm for minimax optimization with engineering applications

Over the past few years a number of researchers in mathematical programming and engineering became very interested in both the theoretical and practical applications of minimax optimization. The purpose of the present paper is to present a new method of solving the minimax optimization problem and at the same time to apply it to nonlinear programming and to three practical engineering problems. The original problem is defined as a modified leastpth objective function which under certain conditions has the same optimum as the original problem. The advantages of the present approach over the Bandler-Charalambous leastpth approach are similar to the advantages of the augmented Lagrangians approach for nonlinear programming over the standard penalty methods.This work was supported by the National Research Council of Canada under Grant A4414, and from the University of Waterloo.     

On conditions for optimality of the nonlinearl 1 problem

The purpose of this paper is to present necessary and sufficient conditions for optimality in the nonlinearl ₁ problem. Furthermore, the relationship of thel ₁ problem and the Pietrzykowski's approach to solve the nonlinear programming problem is discussed in detail.     

Nonlinear programming using minimax techniques

A minimax approach to nonlinear programming is presented. The original nonlinear programming problem is formulated as an unconstrained minimax problem. Under reasonable restrictions, it is shown that a point satisfying the necessary conditions for a minimax optimum also satisfies the Kuhn-Tucker necessary conditions for the original problem. A leastpth type of objective function for minimization with extremely large values ofp is proposed to solve the problem. Several numerical examples compare the present approach with the well-known SUMT method of Fiacco and McCormick. In both cases, a recent minimization algorithm by Fletcher is used.This paper is based on work presented at the 5th Hawaii International Conference on System Sciences, Honolulu, Hawaii, 1972. The authors are greatly indebted to V. K. Jha for his programming assistance and J. H. K. Chen who obtained some of the numerical results. This work was supported in part by the National Research Council of Canada under Grant No. A7239, by a Frederick Gardner Cottrell Grant from the Research Corporation, and through facilities and support from the Communications Research Laboratory of McMaster University.     

Minimal systems of binomial generators and the indispensable complex of a toric ideal

Let be a vector configuration and its corresponding toric ideal. The paper consists of two parts. In the first part we completely determine the number of different minimal systems of binomial generators of . In the second part we associate to a simplicial complex . We show that the vertices of correspond to the indispensable monomials of the toric ideal , while one dimensional facets of with minimal binomial -degree correspond to the indispensable binomials of .

     

Symmetry and singularity analyses of some equations of the fifth and sixth order in the spatial variable arising from the modelling of thin films

In the modelling of the flow of thin films higher-order derivatives in the spatial variable are introduced to model nonlinear effects. We examine nonlinear evolution equations of the fifth and sixth orders in the spatial variable from the viewpoint of Lie symmetry analysis. Values of the parameters which allow for a greater number of Lie point symmetries are identified. As the equations can be recast in potential form, we consider their potential symmetries. We also consider the singularity properties of the corresponding steady-state equations.     

A lower bound for the controlling parameters of the exact penalty functions

The purpose of this paper is to present new exact penalty functions and discuss their properties. A lower bound on the controlling parameters is given, for which above this value, the optimum of the exact penalty function coincides with the optimum of the nonlinear programming problem.This work was supported by the National Research Council of Canada under Grant A4414.     

Temperature dependence of positron annihilation parameters in tin

The positron mean life and the Doppler broadening of the annihilation line were measured in tin from ?196°C to 220°C. A small increase with temperature was observed in the values of these parameters.