Optimization of positive generalized polynomials under constraints.

The problem of maximizing a non-negative generalized polynomial of degree at most p on the l p-sphere is shown to be equivalent to a concave one. Arguments where the maximum is attained are characterized in connection with the irreducible decomposition of the polynomial, and an application to the labelling problem is presented where these results are used to select the initial guess of a continuation method.

[1]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[2]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[3]  Azriel Rosenfeld,et al.  Scene Labeling by Relaxation Operations , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Olivier D. Faugeras,et al.  Improving Consistency and Reducing Ambiguity in Stochastic Labeling: An Optimization Approach , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  Robert M. Haralick,et al.  Structural Descriptions and Inexact Matching , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Steven W. Zucker,et al.  On the Foundations of Relaxation Labeling Processes , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Donald Geman,et al.  Bayes Smoothing Algorithms for Segmentation of Binary Images Modeled by Markov Random Fields , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  G. B. Smith,et al.  Preface to S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images” , 1987 .

[10]  Marc Berthod,et al.  Deterministic pseudo-annealing: a new optimization scheme applied to texture segmentation , 1992, Proceedings., 11th IAPR International Conference on Pattern Recognition. Vol.II. Conference B: Pattern Recognition Methodology and Systems.