Uniform estimates for a variational problem with small parameters

Communicated by J. M. Ball     

Rearrangements of (0–1) matrices

Let ℬ(m) be the set of all then-square (0–1) matrices containingm ones andn ²−m zeros, 0<m<n ². The problem of finding the maximum ofs(A ²) over this set, wheres(A ²) is the sum of the entries ofA ²,A ∈ ℬ (m) is considered. This problem is solved in the particular casesm=n ² −k ² andm=k ²,k ²>(n ²/2). This paper forms part of a thesis in partial fulfillment of the requirements for the degree of Doctor of Science at the Technion-Israel Institute of Technology. The author wishes to thank Professor B. Schwarz and Dr. D. London for their help in the preparation of this paper.     

C-Programming: An outline

This paper presents the essentials of a method designed to solve optimization problems whose objective functions are of the form g(x)+ ψ(u(x)), where ψ is differentiable and either concave or convex. It is shown that solutions to such problems can be obtained through the solutions of the Lagrangian problem whose objective function is of the form g(x)+ λu(x).     

Determination of Economic Packaging Set-up Frequency of Jointly Replenished Items

This paper deals with the problem of determining the economic operating policy for inventory items which are manufactured jointly but packaged individually. The proposed new approach is very simple and efficient. An extensive simulation study is presented so that the results of several heuristics (based on a wide range of data, measuring the number of optimal solutions, average error and maximum error) can be compared.     

C-programming problems: a class of non-linear optimization problems

A method is introduced for the solution of minimization problems possessing objective functions of the form g(x)+?(u(x)), where ? is differentiable and concave. It is shown that a solution to such problems can be obtained through the solution of the Lagrangian problem whose objective function has the form g(x)+λu(x).     

Numerical radius of positive matrices

We study some properties of the numerical radius of matrices with non-negative entries, and explicit ways to compute it. We also characterize positive matrices with equal spectral and numerical radii, i.e., positive spectral matrices.