Abstract
The Fundamental Theorem of Linear Programming says that if there is a feasible solution, there is a basic feasible solution, and if there is an optimal feasible solution, there is an optimal basic feasible solution. The linear programming problem is thus reduced to searching among the set of basic solutions for an optimal solution. The problem of minimizing or maximizing a sufficiently smooth nonlinear function of variables with no restrictions is essentially an ordinary problem in calculus. The problem of inequality constraints is significantly more complicated in the nonlinear case than in the linear case. A method specifically designed for minimizing is the method of steepest descent.
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