KKT Conditions and Branch and Bound Methods on Pure Integer Nonlinear Programming

Optimization problems are not only formed into a linear programming but also nonlinear programming. In real life, often decision variables restricted on integer. Hence, came the nonlinear programming. One particular form of nonlinear programming is a convex quadratic programming which form the objective function is quadratic and convex and linear constraint functions. In this research designed a completion of a convex quadratic integer programming with Karush Kuhn Tucker conditions which then reduces the integer convex quadratic programming into a linear complementary problem. Then used a modified simplex method and Branch and Bound method to obtain the optimal and integer solution and fulfill all the constraints. The obtained solution by using KKT conditions is a global optimum solution due to the problem studied is convex. This method is effective in finding integer solution with result that is not too far from the initial solution to the problem which is quite simple.