You may solve an optimization problem with the ALIAS library by using one of the following procedures:
Minimize Maximize MinimizeGradient MaximizeGradient MinMax MinMaxGradient.
Note that these procedures are only special variants of the general solving procedures of ALIAS-Maple. Hence most of the parameters setting for these procedures are also valid for the optimization procedures. Specific parameters for these procedure are presented in section 5.3.
In the list of functions that are provided to these procedures the last one must be the function whose extremum are looked for, while the other one are supposed to be constraints. The interval solution that are returned will verify:
You may also us the gradient of the function to be minimize or maximized to improve the efficiency of the procedure. The MinimizeGradient and MaximizeGradient procedures may be used for this purpose and have the same argument than the Minimize and Maximize procedure.
There are also procedures to compute at the same time the minimum and maximum values of a function, eventually under constraint. The Minmax and MinMaxGradient procedures may be used for this purpose. The only difference with the previous procedures is that the arguments should be ended by Min, Max which provide the minimum and maximum of the function (being understood that the function that is considered is always the last in the list, the other one being the constraints).
However in that case a global variable of the ALIAS Maple
library may play an important role:
`ALIAS/stop_minmax. Its default value is set to 0 but:
The flag allow_storage may also be of interest: if set to 1 (default value: 0) the current estimation of the optimum is written in the file .opti in a sequential way.
All these procedures accept optionally as least argument a string Simp that indicates the name of a simplification procedure (see chapter 4) whose C++ code is available in the file Simp.C. Among the simplification procedures provided by ALIAS-Maple the use of the HullIConsistency procedure with the key-word Optimum may be interest for an optimization problem, see section 4.2.1.
You may also specify initial value for the minimum or maximum value of the optimized function by setting `ALIAS/opt_min`, `ALIAS/opt_max`.