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

A. W. Tucker
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A. W. Tucker: Princeton University, Princeton, New Jersey

Operations Research, 1957, vol. 5, issue 2, 244-257

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.

Date: 1957
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