The aim of this note is to present the necessary optimality conditions for a model (in closed population) of an immunizing disease similar to hepatitis B following. We study the impact of medical tests and controls involved in curing this kind of immunizing disease and deduced a well posed adjoint system if there exists an optimal control.

In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a longtime smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is c...

It has been observed empirically that a simple linearization method applied to the problem of finding maximal solutions to systems of linear inequalities frequently terminates in one step. This is normally a Kuhn-Tucker point, and depending on the starting point, can be a global solution. An explanation of this phenomenon is given, and this is illustrated by examples.

Nervous Children. By Beverly R. Tucker, M.D. Boston: Richard G. Badger, 1916. Pp. 147. Dr. Tucker writes as a neurologist, but not for neurologists. What strikes most forcibly a student of psychology is his apparent failure to grasp the psychological problems of nervous and mentally deficient children, and his lack of any reference to the large and growing psychological literature on their trai...

This paper is devoted to studying the robust isolated calmness of the Karush– Kuhn–Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both t...

We report on the use of a quadratic programming technique in recent and upcoming spectrum auctions in Europe. Specifically, we compute a unique point in the core that minimizes the sum of squared deviations from a reference point, for example, from the Vickrey-Clarke-Groves payments. Analyzing the Karush-Kuhn-Tucker conditions, we demonstrate that the resulting payments can be decomposed into a...

In this paper, we establish strong complementary approximate Karush- Kuhn-Tucker (SCAKKT) sequential optimality conditions for multiobjective optimization problems with equality and inequality constraints without any constraint qualifications introduce a weak qualification which assures the equivalence between SCAKKT Karush-Kuhn-Tucker (J Optim Theory Appl 80 (3): 483-500, 1994) problems.

Any real number x in the unit interval can be expressed as a continued fraction x = [n1, ..., nN , ...]. Subsets of zero measure are obtained by imposing simple conditions on the n N . By imposing n N ≤ m ∀ N ∈ IN , Jarnik defined the corresponding sets Em and gave a first estimate of dH(Em), dH the Hausdorff dimension. Subsequent authors improved these estimates. In this paper we deal with dH(...

A Multi-item inventory model with increasing holding cost, under available limited storage space and total investment cost is considered in this paper. The varying holding cost is considered to be a continuous function of production quantity. A demand dependent on unit cost has been considered and this unit cost is taken in fuzzy environment. The model is solved using Kuhn-Tucker conditions met...

The interval linear programming (IvLP) 1 is a method for decision making under uncertainty. A weak feasible solution to IvLP is called weakly optimal if it is optimal for some scenario of the IvLP. One of the basic and difficult tasks in IvLP is to check whether a given point is weak optimal. In this paper, we investigate linear programming problems with interval right-hand side. Some necessary...