Triplet of Fibonacci Duals : Identical Duality (Study on Nonlinear Analysis and Convex Analysis)

Abstract

We consider three pairs of quadratic optimization problems from a view point of identical duality. An identity (CI) [n-1]∑[k=1][(X[k-1]-x[k])μ[k]+x[k](μ[k]-μ[k+1])]+(x[n-1]-x[n])μ[n]+x[n]μ[n]＝x₀μ₁ is called complementary. We show that a complementary identity via conditional complementarity produces a pair of conditional minimization (primal) problem and conditional maximization (dual) problem, together with an equality condition. It is shown that both the problems have an identical optimal solution (point and value). Moreover, we show that a primal and its dual satisfyFibonacci Identical Duality.