Abstract:  The canonical duality theory is developed recently with a one to one corresponding between a dual and a primal feasible solution. Initially it is shown computationally efficient using the sufficient conditions of the strong duality property for manyproblems such as the 0−1quadratic programming, the multi-integer quadratic programming, and the sum-of-quadratic-ratios problem. Moreover, we can find that all these models are or can be transformed to quadratic programs with quadratic constraints.
  In this talk, we will outline our recent work on the modeling and applications of the canonical duality approaches to quadratic programs. Some well-known problems can be modeled into the quadratic programs, for example, the max-cut, the 0-1 quadratic programming, the sum-of-quadratic-ratios programming, the non-convex quadratic programming over linear constraints etc.
  After a brief introduction of the canonical duality theory, we provide with a canonical duality optimization model by only considering the positive definite region. Analytic properties are given for the canonical duality function.
  Aquadratic programming with a non-convex quadratic constraint is a simple case of quadratic programs. With the application of the canonical duality approaches, it is shown that it is polyno-mially solvable under duality Slater condition and the global primal minimizer can be easily got. Acanonical duality iteration algorithm is provided for the quadratic programming over linear constraints, which converges to a Karush-Kuhn-Tucker point. Some optimality properties are discussed for the canonical duality approach.