Journal ArticleDOI
An Extension of Lawler and Bell's Method of Discrete Optimization with Examples from Capital Budgeting
TLDR
This paper extends Lawler and Bell's method for solving integer linear programs with 0--1 decision variables so that it can be generally applied to integer quadratic programs.Abstract:
The usefulness of integer programming as a tool of capital budgeting hinges on the development of an efficient solution technique. An algorithm based on partial enumeration has been developed by E. L. Lawler and M. D. Bell for solving integer linear programs with 0--1 decision variables; however their algorithm is not general enough to deal with all problems in which the objective function is quadratic. This paper extends Lawler and Bell's method so that it can be generally applied to integer quadratic programs. The new algorithm is illustrated by examples from capital budgeting.read more
Citations
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Journal ArticleDOI
Improved linear integer programming formulations of nonlinear integer problems
TL;DR: In this article, the authors present new formulation techniques for capturing the essential nonlinearities of the problem of interest, while producing a significantly smaller problem size than the standard techniques, which can be used to reduce the number of variables and constraints.
Journal ArticleDOI
Technical Note-Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program
Fred Glover,Eugene Woolsey +1 more
TL;DR: Rules are given that permit 0-1 polynomial programming problems to be converted to0-1 linear programming problems in a manner that replaces cross-product terms by continuous rather than integer variables, so that the continuous variables automatically receive integer values.
Journal ArticleDOI
A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems
Warren P. Adams,Hanif D. Sherali +1 more
TL;DR: A new linearization technique is presented for the solution of linearly constrained zero-one quadratic programming problems, demonstrated to yield a tighter continuous or linear programming relaxation than is available through other methods.
Journal ArticleDOI
An improved branch and bound algorithm for mixed integer nonlinear programs
Brian Borchers,John E. Mitchell +1 more
TL;DR: An improved branch and bound code for zero-one mixed integer nonlinear programs with convex objective functions and constraints with Lagrangian duality is described.
Book ChapterDOI
Methods of Nonlinear 0-1 Programming
TL;DR: The main results of various approaches to the solution of nonlinear programs in 0-1 variables, as well as some of the many applications, are summarized.
References
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Journal ArticleDOI
Chance-Constrained Programming
TL;DR: The paper presents a method of attack which splits the problem into two non-linear or linear programming parts, i determining optimal probability distributions, ii approximating the optimal distributions as closely as possible by decision rules of prescribed form.
Journal ArticleDOI
Capital Budgeting of Interrelated Projects: Survey and Synthesis
TL;DR: In this paper, a survey of techniques available to handle the important and generally neglected problem of project interrelationships such as mutual exclusion and interdependencies is presented, and a dynamic programming code for the multidimensional 0-1 knapsack problem is also presented.
Journal ArticleDOI
A Method for Solving Discrete Optimization Problems
E. L. Lawler,M. D. Bell +1 more
TL;DR: This paper describes a simple, easily-programmed method for solving discrete optimization problems with monotone objective functions and completely arbitrary (possibly nonconvex) constraints that is computationally feasible for problems in which the number of variables is fairly small.
Related Papers (5)
Letter to the Editor-Reduction of Integer Polynomial Programming Problems to Zero-One Linear Programming Problems
Technical Note-Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program
Fred Glover,Eugene Woolsey +1 more