Average Group of functions defined on Loss and Gain includes the following functions:

 

Full Name

Brief Name

Short Description

Average Loss

avg

Average Loss obtained by averaging Linear Loss scenarios, i.e., it is a linear function with coefficients obtained by averaging  coefficients of Linear Loss scenarios.

Average Gain

avg_g

Average Gain obtained by averaging -(Linear Loss ) scenarios, i.e., it is a linear function with coefficients obtained by averaging  coefficients of  -(Linear Loss) scenarios.

Average Max

avg_max_risk

There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Loss scenarios function is calculated by maximizing losses over Linear Loss functions (over M functions for every scenario).  Average Max is calculated by averaging Maximum Loss scenarios.

Average Max for Gain

avg_max_risk_g

There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Gain scenarios function is calculated by maximizing losses over  -(Linear Loss)  functions for every scenario (over M functions for every scenario).  Average Max for Gain is calculated by averaging Maximum Gain scenarios.

Average Max Deviations

avg_max_dev

There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Deviation scenarios function is calculated by maximizing losses over (Linear Loss) -  (Average Linear Loss over scenarios) functions (over M functions for every scenario).  Average Max Deviation is calculated by averaging Maximum Deviation scenarios.

Average Max Deviation for Gain

avg_max_dev_g

There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Gain Deviation scenarios function is calculated by maximizing losses over -(Linear Loss)+  (Average Linear Loss over scenarios) functions (over M functions for every scenario).  Average Max Gain Deviation is calculated by averaging Maximum Gain Deviation scenarios.

Average Recourse

avg(recourse(.))

Average of  Recourse  scenarios.  Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

Average Gain Recourse

avg_g(recourse(.))

Average of -(Recourse ) scenarios.  Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

 

Remarks

1.Functions from the Average Group are calculated with double precision.
2.Any function from this group may be called by its "brief name" or by "brief name" with "optional name"
The optional name of any function from this group may contain up to 128 symbols.
Optional names of these functions may include only alphabetic characters, numbers, and the underscore sign, "_".
Optional names of these functions are "insensitive" to the case, i.e. there is no difference between low case and upper case in these names.