Bo Peng

Solution of Binary-Constrained Quadratic-Defined Optimization Problems by a Progressive Integer Programming Method

Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , ,

Extending a classic result of Giannessi and Tomasin [\textit{Lecture Notes in Comput. Sci. 3}, Springer, 1973, pp. 437–449], this paper shows that a binary-constrained quadratic-defined optimization problem can be formulated as a binary-constrained linear program with linear complementarity constraints (Bi-LPCC). The term “quadratic-defined problems” encompasses many problems that are defined by quadratic functions in the … Read more

Tighter yet more tractable relaxations and nontrivial instance generation for sparse standard quadratic optimization

Categories (Mixed) Integer Nonlinear Programming, Cone Programming, Semi-definite Programming Tags , , , ,

The Standard Quadratic optimization Problem (StQP), arguably the simplest among all classes of NP-hard optimization problems, consists of extremizing a quadratic form (the simplest nonlinear polynomial) over the standard simplex (the simplest polytope/compact feasible set). As a problem class, StQPs may be nonconvex with an exponential number of inefficient local solutions. StQPs arise in a … Read more

On Tractable Convex Relaxations of Standard Quadratic Optimization Problems under Sparsity Constraints

Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming, Semi-definite Programming Tags , , , ,

Standard quadratic optimization problems (StQPs) provide a versatile modelling tool in various applications. In this paper, we consider StQPs with a hard sparsity constraint, referred to as sparse StQPs. We focus on various tractable convex relaxations of sparse StQPs arising from a mixed-binary quadratic formulation, namely, the linear optimization relaxation given by the reformulation-linearization technique, … Read more