Kuhn-Tucker theorem

Hint. Use the Kuhn-Tucker theorem. Cf. Horn Jackson (1972). 

If the problem is formulated with one single criterion F x,) with the constraints (12.1), then the necessary conditions for a maximum are derived from the Kuhn-Tucker theorem (Kuhn and Tucker (1951) and have the following form ... 

The compromise set may be determined from the Kuhn-Tucker theorem (equation 12.2) in which function P from equation 13.3 is expressed by... 

The Kuhn-Tucker theorem plays a central role in giving conditions for an optimum solution to a general constrained optimization problem. For the primal problem mentioned above, these conditions may be stated... 

Since there is one control variable, by Theorem 3 feasibility measure is determined by two active constraints. Since for each pair of active constraints the corresponding Kuhn-Tucker multipliers Am must be nonnegative [Eq. (35e)], each pair of active constraint functions must have gradients of opposite sign [Eq. (35b)]. Thus the potential sets of active constraints are... 

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