A UNIFIED APPROACH OF OPTIMALITY CRITERIA AND MATHEMATICAL PROGRAMMING VIA THE MAXIMUM ENTROPY METHOD

摘要

The following conclusions can be drawn from this work: 1. An approach based on a probabilistic approach of the optimality criteria has been revisited and enhanced. 2. The new method can be understood as a sequence of linear problems technique. 3. For linear problems constitutes a version of the so called interior point methods, requires very few iterations and, therefore, is an alternative to the simplex method. 4. As the procedure needs the use of first order derivatives it can be also seen as a new gradient based procedure. 5. The new algorithm transforms the optimization problem into the task of solving several times a system of linear equations with a number of unknowns equal to the number of design variables and independent of the number of constraints. 6. The formulation created has been applied to several structural optimization problems and the accuracy of numerical results is very promising.