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tv 00 o -.J optimizat~on scheme has its unique properties making it adapt- able to sp,ecific problems, although many techniques when -':'!: sufficien~ly understood can be modified to extend their .~ applicabili ty. Most Qonditions encountered in irrigated agriculture involve mathematical formulations which are nonlinear in both the objective function and the constraints. Furthermore, the constraining functions may be mixtures of linear and nonlinear equalities and inequalities. Without simplifying these problems or radically changing existing optimization techniques, it is possible to derive solutions based upon what Wilde and Beightler (1967) describe as the "differential approach." Most techniques for selecting the optimal policy do so by successively improving a previous estimate until no betterment is possible. These may be classified as direct or indirect methods depending on whether they start at a feasible point and stepwise mqve toward the optimum or solve a set of equations which cont~in the optimum as a root. In a majority of cases, the differential approach can be used to describe the method. The owtimizing technique used in this effort is called the "Jacobian J;>ifferential Algorithm." Theoretically, it is a generalized elimination procedure which is computationally feasible u~der a wide variety of conditions. The characteristics of convexity are assumed and since the maximization problem is simply the negative of a minimization one, the following discussion.will be limited to the latter case, As in all direct minimizing procedures, the algorithm involves four steps: 1. Evaluate a first feasible solution, xO, which satisfies the problem constraints, The underbar iridicates vector notation and the superscript 0 is used to describe the "old" or initial points; 2. Determine the direction in which to move such that the objective function, y, is decreased most rapidly. This requires a move from x 0 to the new point" xv, in which the superscript v-represents the new pOlnt notation; 3. Find the distance that can be moved without violating any of the problem constraints; and 4. Stop when the optimum is reached. The user is, left only with providing the first feasible solution, step 1. This may seem to be a drawback for the problem, but in real situations a feasible solution already exists as a current policy. SteP 4 is accomplished by an examination of what are now referred to as the "Kuhn-Tucker conditions." These criteria do not indicate whether the procedure has reached a local or global optimum; consequently, it is necessary to derive a means for checking, 9 ., it ! -~ , , ~ ,. ',~ '-Ii , ,I , :~