THE ALTERNATELY FIBONACCI COMPLEMENTARY DUALITY IN QUADRATIC OPTIMIZATION PROBLEM - Iwamoto, S.; Kimura, Y. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
In this paper, we consider a pair of primal and dual quadratic optimization problems, and we compare optimal values and optimal points of both problems. The optimal values and optimal points of both problems have a triple Fibonacci property as follows. (i) The value of maximum and minimum are the same (duality). (ii) The maximum point and the minimum point are two-step alternate Fibonacci sequences (2step alternately Fibonacci). (iii) Both the optimal points constitute alternately two consecutive positive numbers and two consecutive negative numbers of Fibonacci sequence (alternately Fibonacci complement). This triplet is called the alternately Fibonacci complementary duality. Moreover, we show a two-step alternate DA VINCI Code by using optimal points of their quadratic optimization problems, and we propose a method the alternately Fibonacci section to find optimal points for their problems.