Second order necessary and sufficient optimality conditions for bang–bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi–)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadr...

The solution of an optimal power ow (OPF) problem in rectangular form by an interior-point method (IPM) for nonlinear programming is described. When formulated in rectangular form, some OPF variants have quadratic objective and quadratic constraints. Such quadratic features allow for ease of matrix setup and inexpensive incorporation of higher-order information in a predictor-corrector procedur...

This thesis is based on U. Pinkall’s study of the classification of immersions of compact surfaces into R3 up to regular homotopy. The main idea of the classification is to associate to any immersion f a quadratic form qf on the first homology group of the underlying surface Σ with Z2 coefficients, whose associated bilinear form is the nondegenerate intersection form in H1(Σ,Z2), having the pro...

Exact asymptotic behavior is given for high excursion probabilities of a quadratic form zero-mean Gaussian stationary vector process with Pickands’ type covariance matrix in the vicinity zero. The case positive maximum eigenvalue order 1 considered.