Objective in General (Text) Format
Contents
The Objective is represented in the following mathematical form:
Objective = 
,
where
are Functions and 
are coefficients.
Some functions can not be included in linear combinations. For instance functions from Probability group cannot be combined with other functions (see Objective).
Syntax
Full Format of Objective section :
Objective: <objective name> [, linearize = 1 | , quadratic = 1| , function = 1] [<coefficient 1>*] <function 1> ............................... [<coefficient K>*] <function K> |
Short Format of Objective section :
[linearize = 1 | quadratic = 1 | function = 1] [<coefficient 1>*] <function 1> ............................... [<coefficient K>*] <function K> |
Description
In Full Format the Objective section must begin with the keyword "Objective" and include Objective name. This line may optionally include parameters "linearize", or "quadratic", or "function". Only one of these two parameters may be set. By default, "linearize=0", "quadratic = 0", and "function = 0".
PSG functions included in Objective are placed with coefficients (starting from the second line, one function with coefficient per line). If coefficient = 1, then the coefficient can be skipped.
In Short Format the first line of the Objective section may optionally include parameters "linearize", or "quadratic", or "function". Only one of these two parameters should be included. By default, "linearize=0", "quadratic = 0", and "function = 0". Other lines contain PSG functions with coefficients (one function with coefficient per line).
The text in italics in brackets <objective name> is the objective name:
| • | Contains up to 128 symbols; |
| • | Begins with the string “objective_”; |
| • | Includes only alphabetic characters, numbers, and the underscore sign, “_”. |
Option "linearize = 1" or "quadratic = 1" informs solver that the objective should be linearized or have quadratic approximation.
Option "linearize = 1" presents a piecewise linear function with a system of linear constraints (if it is possible), otherwise this option is ignored. The linearization option may speed up optimization, if number of scenarios in Matrices of Scenarios in functions in Objective does not significantly exceed the number of variables in the Objective.
The option "quadratic = 1" impacts the solving process if the Problem is quadratic and VAN solver is used, otherwise it is ignored. With this option, VAN solver treats function in objective as quadratic, i.e., (x,Gx), where G is a positive definite matrix. If the Problem is quadratic (with quadratic objective and linear constraints) and "quadratic = 1", VAN solver optimizes the Problem with a specialized quadratic optimization algorithm (which may speed up the optimization).
The option "function = 1" has effect only when a problem without constraints is solved by Buldozer solver (see Solver in Text Format). It forces Buldozer to use finite difference scheme to estimate gradient of objective instead of using usual analytic calculation. Buldozer starts with rough estimation and improves accuracy while it brings nearer optimal point.
The strings in italics in brackets <coefficient 1>,...,<coefficient K> are the coefficients 
.
Values less than -1020 for the coefficients are treated as -∞, and values larger than 1020 are treated as +∞.
Text string in square brackets "[]" can be skipped, if the coefficient equals 1. For example, the string "<coefficient K>* " can be skipped if 
.
The strings in italics in brackets <function 1>,...,<function K> denote functions (see Description of Function in Text Format).
Example
maximize
avg_g(matrix_h)
-1.3571*pm2_pen(-10, matrix_h)
+1.3571*pm2_pen(-3, matrix_h)
Constraint: == 1
linear(matrix_budget)
Box: >= 0, <= 0.3
Solver: precision = 9