Triplet of Fibonacci Duals : with or without constraint (New Developments on Mathematical Decision Making Under Uncertainty)

Abstract

We consider a dual relation between minimization (primal) problem and maximization (dual) problem from a view point of complementarity. An identity (CI) [n-1]Σ[k=1][(xk-1 - xk)μk + xk(μk - μk+1)] + (xn-1 - xn)μn + xnμn = x0μ1 is called complementary [20, 22]. We present three types of complementary identities, which take a fundamental role in analyzing respective pairs of primal and dual. Moreover, we show that a primal and its dual satisfy Fibonacci Complementary Duality [18, 19, 21, 22].