Constraints binding

Geometry of a constrained optimization problem. The feasible region lies within the binding constraints plus the boundaries themselves. 

The preceding results may be stated in algebraic terms. For V/ to lie within the cone described earlier, it must be a nonnegative linear combination of the negative gradients of the binding constraints that is, there must exist Lagrange multipliers u such that... 

Consequently, most of the optimisation variables have the tendency to migrate to the bounds, and only a limited number of variables are free to move inside the space of variations. Often the constraints are expressed as optimum performance, so that the optimisation procedure will try to fulfil them as active (binding) constraints. 

In Figure 18.2b, an upper bound is placed on x, and that bound is below the value at the maximum value of the objective function. Therefore, the optimal value of x is its upper bound, and the constraint is referred to as a binding constraint. 

F ure 18.2 Nonlinear objective function (a) subject to a slack constraint (b) subject to a binding constraint. 

Separation of contact and pseudocontact or ligands with binding constraints 47... 

Complexes with sterically rigid ligands or ligands with binding constraints 4.4.1. [R(dpa)i] and [R(mdpa) ] complexes ... 

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