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1.1 Definitions

The goal of an optimization problem can be formulated as follows: find the combination of parameters (independent variables) which optimize a given quantity, possibly subject to some restrictions on the allowed parameter ranges. The quantity to be optimized (maximized or minimized) is termed the objective function; the parameters which may be changed in the quest for the optimum are called control or decision variables; the restrictions on allowed parameter values are known as constraints.

A maximum of a function f is a minimum of -f. Thus, the general optimization problem may be stated mathematically as:

where is the objective function, is the column vector of the n independent variables, and is the set of constraint functions. Constraint equations of the form are termed equality constraints, and those of the form are inequality constraints. Taken together, and are known as the problem functions.