IMPROVED LINEAR INTEGER PROGRAMMING FORMULATIONS OF NONLINEAR INTEGER PROBLEMS
@article{Glover1975IMPROVEDLI, title={IMPROVED LINEAR INTEGER PROGRAMMING FORMULATIONS OF NONLINEAR INTEGER PROBLEMS}, author={Fred W. Glover}, journal={Management Science}, year={1975}, volume={22}, pages={455-460} }
A variety of combinatorial problems (e.g., in capital budgeting, scheduling, allocation) can be expressed as a linear integer programming problem. However, the standard devices for doing this often produce an inordinate number of variables and constraints, putting the problem beyond the practical reach of available integer programming methods. This paper presents new formulation techniques for capturing the essential nonlinearities of the problem of interest, while producing a significantly…
734 Citations
A level set approach to integer nonlinear optimization
- Mathematics
- 2013
Integer nonlinear optimization programs form a class of very hard problems. Often it is much easier to solve the continuous relaxation. Therefore we are interested in this thesis in identifying…
Mixed Integer Linear Programming Formulation Techniques
- BusinessSIAM Rev.
- 2015
This survey reviews advanced MIP formulation techniques that result in stronger and/or smaller formulations for a wide class of problems.
Nonlinear integer programming for various forms of constraints
- Mathematics
- 1982
A theoretical and computational investigation is made of the performance of a dynamic‐programming‐based algorithm for nonlinear integer problems with various types of constraints. We include linear…
A note on solving quadratic programs using mixed-integer programming
- Computer ScienceComput. Oper. Res.
- 1989
Linear and Integer Programming with Sensitivity Analysis Approach
- Mathematics
- 2013
Linear programming is the name of a branch of applied mathematics that deals with solving optimization problems of a particular form. Linear programming problems consist of a linear cost function or…
LP formulations for mixed-integer polynomial optimization problems
- Mathematics, Computer Science
- 2015
An approximation scheme for the “AC-OPF” problem on graphs with bounded tree-width is obtained and a more general construction for pure binary optimization problems where individual constraints are available through a membership oracle is described.
Solving Mixed Integer Bilinear Problems Using MILP Formulations
- MathematicsSIAM J. Optim.
- 2013
This paper presents the convex hull of the underlying mixed integer linear set and the effectiveness of this reformulation and associated facet-defining inequalities are computationally evaluated on five classes of instances.
An efficient global optimization approach for solving mixed-integer nonlinear programming problems
- MathematicsThe 40th International Conference on Computers & Indutrial Engineering
- 2010
Mixed-integer nonlinear programming (MINLP) problems involving general constraints and objective functions with continuous and integer variables occur frequently in engineering design, chemical…
References
SHOWING 1-10 OF 21 REFERENCES
Technical Note - Converting the 0-1 Polynomial Programming Problem to a 0-1 Linear Program
- Mathematics, BusinessOper. Res.
- 1974
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.
An Extension of Lawler and Bell's Method of Discrete Optimization with Examples from Capital Budgeting
- Computer Science
- 1968
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.
Further Reduction of Zero-One Polynomial Programming Problems to Zero-One linear Programming Problems
- MathematicsOper. Res.
- 1973
This paper gives rules that enable the transformation of a 0-1 polynomial programming problem into a 0-1 linear programming problem to be effected with reduced numbers of constraints. Rules are also…
Quadratic Binary Programming with Application to Capital-Budgeting Problems
- EconomicsOper. Res.
- 1970
The algorithm developed to solve the quadratic binary programming problem and hence necessary to generate the efficient set is based on the concept of implicit enumeration recently introduced by Egon Balas for solution of the binary linear programming problem.
Flows in Arborescences
- Computer Science
- 1971
This paper gives efficient methods for solving four specially structured network problems that arise in connection with certain integer programming methods developed by Cook and Cooper, Hillier, and…
Linear programming and extensions
- Mathematics
- 1963
This classic book looks at a wealth of examples and develops linear programming methods for their solutions and begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them.
Integer Programming and Network Flows
- Psychology
- 1970
Interestingly, integer programming and network flows that you really wait for now is coming. It's significant to wait for the representative and beneficial books to read. Every book that is provided…
Media Selection by Decision Programming
- Business
- 1976
An approach for finding an optimal media mix through decision programming, a technique that can take into account discounting, duplication, and availability of the medium, and that will still find an…
Un algorithme de programmation quadratique en variables binaires
- Mathematics
- 1969
L’accès aux archives de la revue « Revue française d’automatique, d’informatique et de recherche opérationnelle. Recherche opérationnelle » implique l’accord avec les conditions générales…