Lmax is a function which generates convex piecewise linear scenarios depending on a vector of decision variables .

 

Syntax

For calculation of scenarios of Lmax function:

 

 

For optimization problems with risk functions defined by Lmax function:

 

 

Parameters

matrix_m        is a Matrix of Scenarios:

       

 

where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.

.

 

Mathematical Definition

Lmax Function generates convex piecewise linear scenarios:

,

where

M =  number of random Loss Functions (See section Loss and Gain Functions):

,

 = vector of random coefficients for m-th Loss Function;

 = j-th scenario of the random vector ,

is a random function with scenarios:

.

is an argument of function.

 

Remarks

Input data for Lmax is a set of Matrices of scenarios with equal number of scenarios (rows).

Probabilities of scenarios are taken form the first matrix in a list of the set (matrix_1). So an order of matrices in a list is essential.

 

See also

Loss, Gain, Recourse, Sum of Splines Operator