| Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views, given the relative orientation of the two views. Th...

A binary matrix has the consecutive ones property (C1P) if it is possible to order the columns so that all 1s are consecutive in every row. In [McConnell, SODA 2004 768-777] the notion of incompatibility graph of a binary matrix was introduced and it was shown that odd cycles of this graph provide a certificate that a matrix does not have the consecutive ones property. A bound of k + 2 was clai...

We consider semilinear elliptic problems of the form ∆u+g(u) = f(x) with Neumann boundary conditions or ∆u + λ1u + g(u) = f(x) with Dirichlet boundary conditions, and we derive conditions on g and f under which an upper bound on the number of solutions can be obtained.

This paper is devoted to second order necessary optimality conditions for the Mayer optimal control problem when the control set U is a closed subset of R. We show that, in the absence of endpoint constraints, if an optimal control ū(·) is singular and integrable, then for almost every t such that ū(t) is in the interior of U , both the Goh and a generalized LegendreClebsch conditions hold true...

The classical methods for solving initial-boundary-value problems for linear partial differential equations with constant coefficients rely on separation of variables, and specific integral transforms. As such, they are limited to specific equations, with special boundary conditions. Here we review a method introduced by Fokas, which contains the classical methods as special cases. However, thi...

Stability properties of the problem of minimizing a (nonconvex) linear-quadratic function over an Euclidean ball, known as the trust-region subproblem, are studied in this paper. We investigate in detail the case where the linear part of the objective function is perturbed and obtain necessary and sufficient conditions for the upper/lower semicontinuity of the Karush-Kuhn-Tucker point set map a...

This chapter is mainly about William Karush and his role in the Karush-KuhnTucker theorem of nonlinear programming. It tells the story of fundamental optimization results that he obtained in his master’s thesis: results that he neither published nor advertised and that were later independently rediscovered and published by Harold W. Kuhn and Albert W. Tucker. The principal result – which concer...

We study the smoothing method for the solution of generalized semi-infinite optimization problems from (O. Stein, G. Still: Solving semi-infinite optimization problems with interior point techniques, SIAM J. Control Optim., 42(2003), pp. 769–788). It is shown that Karush-Kuhn-Tucker points of the smoothed problems do not necessarily converge to a Karush-Kuhn-Tucker point of the original problem...

Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate strict constraint qualification associated with some sequential optimality c...

A state-defect constraint pairing graph coarsening method is described for improving computational efficiency during the numerical factorization of large sparse Karush–Kuhn–Tucker matrices that arise from the discretization of optimal control problems via an Legendre–Gauss–Radau orthogonal collocation method. The method takes advantage of the particular sparse structure of the Karush–Kuhn–Tucke...