We present new first and second-order optimality conditions for maximizing a function over a polyhedron. These conditions are expressed in terms of the first and second-order directional derivatives along the edges of the polyhedron, and an edge description of the polyhedron. If the objective function is quadratic and edgeconvex, and the constraint polyhedron includes a box constraint, then loc...

GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality (LMI) relaxations of non-convex optimization problems with multivariate polynomial objective function and constraints, based on the theory of moments. In contrast with the dual sum-of-squares decompositions of positive polynomials, the theory of moments allows to detect global optimality of an LMI relaxation...

The finite difference multigrid solution of an optimal control problem associated with an elliptic equation is considered. Stability of the finite difference optimality system and optimalorder error estimates in the discrete L2 norm and in the discreteH1 norm under minimum smoothness requirements on the exact solution are proved. Sharp convergence factor estimates of the two grid method for the...

This paper presents a general theory of network max-min rate assignment as a lexicographic optimization. The model includes multicast and lower bound constraints. The model for multicast allows the sender to send at the maximum rate allowed by the network and the receivers. Equivalent optimality conditions, especially those which can be coded into practical algorithms, are derived. A reference ...

This paper presents an information-theoretic approach to sensor placement that incorporates communication capacity into an optimal formulation. A new formulation is presented that maximizes the information rate achievable by a set of sensors communicating wirelessly to a single collection node. Shannon capacity and the standard radio propagation model are used to model the throughput achievable...

Abstract: The aim of this paper is to develop a new approach for a solution of the continuous-time model matching problem with a static state feedback in the sense of H∞ optimality criterion. The main contribution is to reformulate the H∞ model matching problem in linear matrix inequality settings, to present the solvability conditions and to give a design procedure for a one degree of freedom ...

This paper develops optimal gender assignment theory, an approach to gender assignment couched within the formalism of Optimality Theory [Prince, Alan, Smolensky, Paul, 1993. Optimality Theory: Constraint Interaction inGenerative Grammar. Rutgers University andUniversity of Colorado, Boulder] and drawing on Steinmetz’ [Steinmetz, Donald, 1985. Gender in German and Icelandic: inanimate nouns. In...