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Symposium on Modern Techniques for Extremum Problems---Linear and Nonlinear Programming

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  • A. W. Tucker

    (Princeton University, Princeton, New Jersey)

Abstract

The linear-programming problem of minimizing a linear objective function subject to linear constraints (inequalities and/or equations, some variables nonnegative) is here embedded in the larger problem of minimizing a convex objective function subject to such linear constraints. The enlarged problem is analyzed by sharpened use of classical Lagrange multipliers. An important case is a quadratic objective function in which the second-degree terms are squares with nonnegative coefficients (or can be so reduced). Linear computation is possible for such quadratic programming, as exemplified classically by the Kirchhoff-Maxwell determination of the distribution of (direct) current in an electrical network. Analogies with potential theory are indicated.

Suggested Citation

  • A. W. Tucker, 1957. "Symposium on Modern Techniques for Extremum Problems---Linear and Nonlinear Programming," Operations Research, INFORMS, vol. 5(2), pages 244-257, April.
    • Handle: RePEc:inm:oropre:v:5:y:1957:i:2:p:244-257
    DOI: 10.1287/opre.5.2.244
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