This paper is based on the author’s thesis, “On duality theorems for quasiconvex programming”. In this paper, we investigate duality theorems for quasiconvex programming as generalizations of results in convex programming, and consists of three topics. The first topic is about quasiconjugates and polar sets. The second is about three types of set containment characterizations. The third is abou...

According to the Smolukowski-Kramers approximation, we show that the solution of the semi-linear stochastic damped wave equations μutt (t, x) = u(t, x)−ut (t, x)+ b(x, u(t, x)) + QẆ(t), u(0) = u0, ut (0) = v0, endowed with Dirichlet boundary conditions, converges as μ goes to zero to the solution of the semi-linear stochastic heat equation ut (t, x) = u(t, x)+b(x, u(t, x))+QẆ(t), u(0) = u0, end...

The hierarchical Tucker format is a way to decompose a high-dimensional tensor recursively into sums of products of lower-dimensional tensors. The number of degrees of freedom in such a representation is typically many orders of magnitude lower than the number of entries of the original tensor. This makes the hierarchical Tucker format a promising approach to solve ordinary differential equatio...

We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals.

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...