Non-Convex Quadratic Programming with Box Constraints is a fundamental NP-hard global optimisation problem. Recently, some authors have studied a certain family of convex sets associated with this problem. We prove several fundamental results concerned with these convex sets: we determine their dimension, characterise their extreme points and vertices, show their invariance under certain affine...

This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. From an original idea by Yakubovich, the approach has been developed under a combination of influences from the Western and Russian traditions of control theory. It is shown how a complex system can be described, using integral quadratic constraints (IQC’s) ...

A simple scheme is proposed for handling nonlinear equality constraints in the context of a previously introduced sequential quadratic programming (SQP) algorithm for inequality constrained problems, generating iterates satisfying the constraints. The key is an idea due to Mayne and Polak (Math. Progr., vol. 11, pp. 67{80, 1976) by which nonlinear equality constraints are treated as \"-type con...

Let Q = fx j s i (x) 0; i = 1; : : : ; kg, where s i (x) = a T i x ?x T Q i x ?c i , and Q i is an n n positive semideenite matrix. We prove that the volumetric and combined volumetric-logarithmic barriers for Q are O(p kn) and O(p kn) self-concordant, respectively. Our analysis uses the semideenite programming (SDP) representation for the convex quadratic constraints deening Q, and our earlier...

In this paper, an aggregate production-planning problem is formulated as a stochastic linear quadratic problem with chance constraints on state and control variables. The stochastic model proposed extends the classical aggregate model developed by Holt, Modigliani, Muth and Simon (HMMS). As an example of application, an equivalent deterministic problem is developed from the stochastic model. Th...

In this paper we address the problem of 3D-location estimation based on quadratic-curved features. It is assumed that the true size and true shape of a feature in object space are known, along with its perspective projection in the image plane. In our approach, we decompose the 3D-location-estimation problem into a concatenated process of SD-orientation estimation and 3D-position estimation. In...

This paper presents new techniques for filtering boxes in the presence of an additional quadratic constraint, a problem relevant for branch and bound methods for global optimization and constraint satisfaction. This is done by generating powerful linear and parabolic relaxations from a quadratic constraint and bound constraints, which are then subject to standard constraint propagation techniqu...

Constraints have played an important role in the construction of GUIs, where they are mainly used to define the layout of the widgets. Resizing behavior is very important in GUIs because areas have domain specific parameters such as form the resizing of windows. If linear objective function is used and window is resized then error is not distributed equally. To distribute the error equally, a q...

We propose a necessary and sufficient test to determine whether solution for general quadratic program with two constraints (QC2QP) can be computed from that of specific convex semidefinite relaxation, in which case we say there is no optimality gap. Originally intended solve nonconvex optimal control problem, consider the cost both QC2QP may nonconvex. obtained our test, also ascertains when s...