Geometric Optimization Revisited

Bertrand’s Paradox Revisited: More Lessons about that Ambiguous Word, Random

The Bertrand paradox question is: “Consider a unit-radius circle for which the length of a side of an inscribed equilateral triangle equals 3 . Determine the probability that the length of a ‘random’ chord of a unit-radius circle has length greater than 3 .” Bertrand derived three different ‘correct’ answers, the correctness depending on interpretation of the word, random. Here we employ geomet...

Global optimization of fractional posynomial geometric programming problems under fuzziness

In this paper we consider a global optimization approach for solving fuzzy fractional posynomial geometric programming problems. The problem of concern involves positive trapezoidal fuzzy numbers in the objective function. For obtaining an optimal solution, Dinkelbach’s algorithm which achieves the optimal solution of the optimization problem by means of solving a sequence of subproblems ...

The matrix arithmetic-geometric mean inequality revisited

A Neural Stiefel Learning based on Geodesics Revisited

In this paper we present an unsupervised learning algorithm of neural networks with p inputs and m outputs whose weight vectors have orthonormal constraints. In this setting the learning algorithm can be regarded as optimization posed on the Stiefel manifold, and we generalize the natural gradient method to this case based on geodesics. By exploiting its geometric property as a quotient space: ...

Computational fluid dynamics analysis and geometric optimization of solar chimney power plants by using of genetic algorithm

In this paper, a multi-objective optimization method is implemented by using of genetic algorithm techniques in order to determine optimum configuration of solar chimney power plant. The objective function which is simultaneously considered in the analysis is output power of the plant. Output power of the system is maximized. Design parameters of the considered plant include collector radius (R...