Constraint Violation Function Research Articles

Nonlinear programming without a penalty function

In this paper the solution of nonlinear programming problems by a Sequential Quadratic Programming (SQP) trust-region algorithm is considered. The aim of the present work is to promote global convergence without the need to use a penalty function. Instead, a new concept of a “filter” is introduced which allows a step to be accepted if it reduces either the objective function or the constraint violation function. Numerical tests on a wide range of test problems are very encouraging and the new algorithm compares favourably with LANCELOT and an implementation of Sl1QP.

Detecting independent motion: the statistics of temporal continuity

We consider a problem central in aerial visual surveillance applications; detection and tracking of small, independently moving objects in long and noisy video sequences. We directly use spatiotemporal image intensity gradient measurements to compute an exact model of background motion. This allows the creation of accurate mosaics over many frames, and the definition of a constraint violation function which acts as an indicator of independent motion. A novel temporal integration method maintains confidence measures over long subsequences without computing the optic flow, requiring object models, or using a Kalman filter. The mosaic acts as a stable feature frame, allowing precise localization of the independently moving objects. We present a statistical analysis of the effects of image noise on the constraint violation measure and find a good match between the predicted probability distribution function and the measured sample frequencies in a test sequence.