Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing that if the decision version of mixed-inte...

Quadratic programming can be seen both as a general approach to linear programming and a special class of nonlinear programming. Moreover, Quadratic Programming problems are of utmost importance in a variety of relevant practical fields, such as, portfolio selection. This work presents and develops a novel fuzzy-sets-based method that solves a class of quadratic programming problems with vaguen...

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 ...