Optimization Theory and Computational Methods in Measure Spaces with Applications

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The purpose of this research is the development of theory and computational methods of estimation of probabilistic or non-probabilistic distributions based on optimization in measure spaces with practical applications to statistical science, control engineering or information theory. The bilateral cutting plane method was developed as an efficient algorithmic framework for linear or convex quadratic programming in measure spaces. We have concentrated on the theory for general nonlinear convex programming in the latter half, and applied it to the problem of communication channel capacity in information theory.