DENG, ZHIBIN. Conic Reformulations and Approximations to Some Subclasses of Nonconvex Quadratic Programming Problems. (Under the direction of Dr. Shu-Cherng Fang.) In this dissertation, some subclasses of nonconvex quadratic programming problems are studied. We first study the nonconvex quadratic programming problem over the standard simplex with application to copositive matrix detection. A se...

Quadratic programming can be seen both as a general approach to linear programming and a special class of non-linear programming. Moreover, quadratic programming problems are of utmost importance in an increasing variety of practical fields, such as, regression, efficient production and portfolio selection. As ambiguity and vagueness are natural and ever-present in real-life situations requirin...

An algorithm for monotropic piecewise quadratic programming is developed. It converges to an exact solution in finitely many iterations and can be thought of as an extension of the simplex method for convex programming and the active set method for quadratic programming. Computational results show that solving a piecewise quadratic program is not much harder than solving a quadratic program of ...