Nonlinear Group

Full Name

Brief Name

Short Description

Polynomial Absolute

polynom_abs

Sum of absolute values of components of a vector, i.e., L1 norm of a vector;

Sum of  powers of absolute values of a vector, e.g., (Lp norm)^p 

CVaR Component Positive

cvar_comp_pos

Average of the largest (1-α)% of components of a vector, where 0≤α≤1

CVaR Component Negative

cvar_comp_neg

Average of the largest (1-α)% of components of a -( vector), where 0≤α≤1

CVaR Component Absolute

cvar_comp_abs

Scaled CVaR Norm = Average of the largest  (1-α)% of absolute values of components of a vector, where 0≤α≤1

VaR Component Positive

var_comp_pos

α*I -th value in the ordered  ascending sequence of components of a I-dimensional vector, where 0≤α≤1; e.g., α=0.8, I=100, we order components of the vector and take the component number α*I = 80  

VaR Component Negative

var_comp_neg

α*I -th value in the ordered  ascending sequence of components of a -(I-dimensional vector), where 0≤α≤1; e.g., α=0.8, I=100,  we order components of the -(vector) and take the element number α*I = 80

Maximum Component Positive

max_comp_pos

Maximal  (largest)  component of a vector

Maximum Component Negative

max_comp_neg

Maximal  (largest)  component of -(vector)

Maximum Component Absolute

max_comp_abs

L-infinity norm of a vector, i.e., the largest absolute value of components of the vector

Quadratic Function

quadratic

Quadratic function

Squareroot Quadratic

sqrt_quadratic

Squareroot of Quadratic function

Logarithms Sum

log_sum

Linear combination of logarithms of components of a vector