Horizontal placement of nodes in tree layout or layered drawings of directed graphs can be modelled as a convex quadratic program. Thus, quadratic programming provides a declarative framework for specifying such layouts which can then be solved optimally with a standard quadratic programming solver. While slower than specialized algorithms, the quadratic programming approach is fast enough for ...

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains g...

We describe a branch and bound algorithm for the quadratic assignment problem QAP that uses a convex quadratic programming QP relaxation to obtain a bound at each node The QP subproblems are approximately solved using the Frank Wolfe algorithm which in this case requires the solution of a linear assignment problem on each iteration Our branching strategy makes extensive use of dual information ...

Computational methods are considered for finding a point that satisfies the secondorder necessary conditions for a general (possibly nonconvex) quadratic program (QP). The first part of the paper defines a framework for the formulation and analysis of feasible-point active-set methods for QP. This framework defines a class of methods in which a primal-dual search pair is the solution of an equa...

We consider convex quadratic programs with large numbers of constraints. We distribute these constraints among several parallel processors and modify the objective function for each of these subproblems with Lagrange multiplier information from the other processors. New Lagrange multiplier information is aggregated in a master processor and the whole process is repeated. Linear convergence is e...

We consider three parametric relaxations of the 0-1 quadratic programming problem. These relaxations are to: quadratic maximization over simple box constraints, quadratic maximization over the sphere, and the maximum eigenvalue of a bordered matrix. When minimized over the parameter, each of the relaxations provides an upper bound on the original discrete problem. Moreover, these bounds are eec...

The theory of self-scaled conic programming provides a uniied framework for the theories of linear programming, semideenite programming and convex quadratic programming with convex quadratic constraints. In the linear programming literature there exists a unifying framework for the analysis of various important classes of interior-point algorithms, known under the name of target-following algor...

We show that the robust counterpart of a convex quadratic constraint with ellipsoidal implementation error is equivalent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma in case the two matrices involved can be simultaneously diagonalized. This extension of the S-lemma may also be useful for other purposes. We extend the result to...

A nonconvex generalized semi-infinite programming problem is considered involving parametric max-functions in both, the objective and the constraints. For a fixed vector of parameters, the values of these parametric max-functions are given as optimal values of convex quadratic programming problems. Assuming that for each parameter the parametric quadratic problems satisfy the strong duality rel...

The paper considers a quadratic programming problem with strictly convex separable objective function, single linear constraint, and two-sided constraints on variables. This is commonly called the Convex Knapsack Separable Quadratic Problem, or CKSQP for short. We are interested in an algorithm solving time complexity. papers devoted to this topic contain inaccuracies description of algorithms ...