Skip to main content
SpringerLink
Log in

Discovering inequality conditions in the analytic solution of optimization problems

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

Necessary and sufficient conditions for the problem of maximizing or minimizing a function subject to inequality constraints are given by a set of equalities and inequalities known as the Kuhn-Tucker conditions. These conditions can provide an analytic solution to the optimization problem if the artificial variables known as Lagrange multipliers can be eliminated. However, this is tedious to do by hand. This paper develops a computer program to assist in the solution process which combines symbolic computation and automated reasoning techniques. The program may also be useful for other problems involving algebraic reasoning with inequalities which employ general functions or symbolic parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Avriel, W. E. Diewert, S. Schaible, and I. Zang, Generalized Concavity. Plenum Press, New York, 1988.

    Google Scholar 

  2. William J., Baumol, Economic Theory and Operations Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1977.

    Google Scholar 

  3. Robert E. Beam and Stanley N. Laiken, Introduction to Federal Income Taxation in Canada. CCH Canadian, 1987.

  4. A. Bundy and B. Welham, ‘Using meta-level inference for selective application of multiple rule sets in algebraic manipulation’, Artificial Intelligence 16, 1981.

  5. Bruce W. Char, Gregory J. Fee, Keith O. Geddes, Gaston H. Gonnet, and Michael B. Monagan, ‘A tutorial introduction to Maple’, Journal of Symbolic Computation 2(2), 179–200, 1986.

    Google Scholar 

  6. B. W. Char, K. O. Geddes, G. H. Gonnet, and S. M. Watt, Maple User's Guide. Watcom Publications, Waterloo, Ontario, 1985.

    Google Scholar 

  7. D. G. Luenberger, Introduction to Linear and Nonlinear Programming. Addison-Wesley, 1984.

  8. A. Macnaughton, ‘Minimizing tax on capital gains on principal residences: a mathematical approach’, 1986. Paper presented at the annual meeting of the Canadian Academic Accounting Association.

  9. P. Strooper, B. W. Char, and A. Macnaughton, A Theorem Prover for Inequalities to Discover Conditions on the Analytical Solution of Optimization Problems, CS-87-18, Technical Report, University of Waterloo, Computer Science Department, 1987.

  10. M. H. van Emden and R. G. Goebel, Waterloo UNIX Prolog User's Manual version 2.0. Waterloo, Ontario, Canada, 1985.

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Tennessee, 37996-1301, Knoxville, TN, USA

    Bruce W. Char

  2. School of Accountancy, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Alan R. Macnaughton

  3. Dept. of Computer Science, University of Victoria, V8W 2Y2, Victoria, British Columbia, Canada

    Paul A. Strooper

Authors
  1. Bruce W. Char
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan R. Macnaughton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paul A. Strooper
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Char, B.W., Macnaughton, A.R. & Strooper, P.A. Discovering inequality conditions in the analytic solution of optimization problems. J Autom Reasoning 5, 339–362 (1989). https://doi.org/10.1007/BF00248323

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00248323

Key words

Search

Navigation