Strong Duality for General Quadratic Programs with Quadratic Equality Constraints

In this article, by ‘general quadratic program’ we mean an optimization problem, in which all functions involved are quadratic or linear and local optima can be different from global optima. For a class of general quadratic optimization problems with quadratic equality constraints, the Lagrangian dual problem is constructed, which is a semi-infinite linear program, or equivalently, a copositive program, i.e., a conic program over the closed convex cone of copositive matrices. Solvability of both primal and dual problems and conditions for strong duality are then investigated in connection with some results from nonlinear parametric optimization.