The paper presents a numerical procedure for solving a class of optimal control problems for heterogeneous systems. The latter are described by parameterized systems of ordinary differential equations, coupled by integrals along the parameter space. Such problems arise in economics, demography, epidemiology, management of biological resources, etc. The numerical procedure include discretization...

Given an a ne system on a full-dimensional polytope, the problem of reaching a particular facet of the polytope, using continuous piecewise-a ne state feedback is studied. Necessary conditions and su cient conditions for the existence of a solution are derived in terms of linear inequalities on the input vectors at the vertices of the polytope. Special attention is paid to a ne systems on full-...

Several new observations which lead to new correctness proofs of two known algorithms (Hu-Tucker and Garsia-Wachs) for construction of optimal alphabetic trees are presented. A generalized version of the Garsia-Wachs algorithm is given. Proof of this generalized version works in a structured and illustrative way and clari es the usually poorly-understood behavior of both the Hu-Tucker and Garsi...

The purpose of this paper is to consider the Mond-Weir type dual model for a class of non-smooth multiobjective semi-infinite programming problem. In this work, we use generalization of convexity namely ( , ) G F θ − convexity and Kuhn-Tucker constraint qualification, to prove new duality results for such semi-infinite programming problem. Weak, strong and converse duality theorems are derived....

This note is focused on a bounded control problem with boundary conditions. The control domain need not be convex. First-order necessary condition for optimality is obtained in the customary form of the maximum principle, and second-order necessary condition for optimality of singular controls is derived on the basis of second-order increment formula using the method of increments along with li...

The residence time measures the time spent by a water parcel or a pollutant in a given water body and is therefore widely used in environmental studies. The adjoint method introduced by Delhez et al. (2004) to compute this diagnostic is revised here to take into account the effect of the initialization and of the boundary conditions. In addition to the equation for the mean residence time, it i...

By virtue of convexification techniques, we study best approximations to a closed set C in a Hilbert space as well as perturbation conditions relative to C and a nonlinear inequality system. Some results on equivalence of the best approximation and the basic constraint qualification are established.

Recently, a number of authors have presented several geometries for rankstructured matrix and tensor spaces, namely the set of matrices or tensors with fixed matrix, Tucker or TT rank. In this talk we present a unifying approach for establishing a smooth, differential structure on the set of tensors with fixed hierarchical Tucker rank. Our approach describes this set as a smooth submanifold, gl...

The Gibbs conditions of stable thermodynamic equilibrium are formulated for nonlinear thermoelastic materials, based on the constrained minimization of four fundamental thermodynamic potentials. Sufficient conditions for incremental stability are stated in each case. The previously unexplored connections between the second-order variations of thermodynamic potentials are used to establish the c...

A new algorithm is presented to solve both the finitehorizon time-varying and infinite-horizon timeinvariant discrete-time optimal reduced-order linear quadratic Gaussian (LQG) problem. In both cases the first order necessary optimality conditions can be represented by two non-linearly coupled discrete-time Lyapunov equations, which run forward and backward in discrete time. The algorithm itera...