% file:         METR95-13
% author:       Tomomi MATSUI 
% organization: Math. Eng. #2 Lab. (Tomomi MATSUI)
% email:        tomomi@misojiro.t.u-tokyo.ac.jp
% title:        NP-hardness of Linear Multiplicative Programming
%               and Related Problems
% keywords:     NP-hard, minimization of products,
%               linear multiplicative programming,
%               linear fractinal programming, 
%               multi-ratio programming
% language:     English

@techreport   {METR95-13,
    AUTHOR="T. Matsui",
    TITLE="NP-hardness of Linear Multiplicative Programming
           and Related Problems",
    YEAR=1995,
    INSTITUTION="University of Tokyo",
    TYPE="Research Report \mbox{METR} 95-13,
          Dept. of Mathematical Engineering and Information Physics,
          Faculty of Engineering"}

\begin{abstract}
The linear multiplicative programming problem
  minimizes a product of two (positive) variables
 subject to linear inequality constraints.
In this paper,
    we show NP-hardness of
    linear multiplicative programming problems
    and related problems.
\end{abstract}