An algorithm for piece-wise indefinite quadratic programming problem

An indefinite quadratic programming problem is a mathematical programming problem which is a product of two linear factors. In this paper, the piece-wise indefinite quadratic programming problem (PIQPP) is considered. Here, the objective function is a product of two continuous piecewise linear functions defined on a non-empty and compact feasible region. In the present paper, the optimality criterion is derived and explained in order to solve PIQPP. While solving PIQPP, we will come across certain variables which will not satisfy the optimality condition. For these variables, cases have been elaborated so as to move from one basic feasible solution to another till we reach the optimality. An algorithmic approach is proposed and discussed for the PIQPP problem. A numerical example is presented to decipher the tendered method.