Table (List) of Deterministic Functions

Full Name

Brief Name

Short Description

Variable

variable

Linear function including only one variable

Linear

linear

Linear function with many variables

Linear Multiple

linearmulti

Set of linear functions (used for building multiple linear constraints)

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

Logarithms Exponents Sum

logexp_sum

Likelihood function in Logistic Regression

Full Name

Brief Name

Short Description

Cardinality Positive

cardn_pos

Number of components of a vector exceeding some threshold

Cardinality Negative

cardn_neg

Number of components of -(vector) exceeding some threshold

Cardinality

cardn

Number of absolute values of components of a vector exceeding some threshold

Buyin Positive

buyin_pos

Number of components of a vector exceeding  threshold_1 and below  threshold_2

Buyin Negative

buyin_neg

Number of components of -(vector) exceeding  threshold_1 and below  threshold_2

Buyin

buyin

For a finite dimension vector, buyin equals the number components satisfying two conditions: 1) absolute value of a component exceeds  threshold_1; 2) if a component is positive, then its absolute value is below  threshold_2, otherwise its absolute value is  below  threshold_3

Fixed Charge Positive

fxchg_pos

Sum of fixed changes for components of a vector exceeding some thresholds

Fixed Charge Negative

fxchg_neg

Sum of fixed changes for components of -(vector) exceeding some thresholds

Fixed Charge

fxchg

Sum of fixed changes for absolute values of components of a vector exceeding some thresholds

Full Name

Brief Name

Short Description

L1 Norm

polynom_abs

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

L2 Norm

sqrt_quadratic

Squareroot of sum of squares of components of a vector, i.e., L2 norm of a vector

Lp Norm

lp_norm

p-th root of sum of p-th powers of absolute values of a vector components (for version 2.2 only)

L-Infinity Norm

max_comp_abs

The largest absolute value of components of a vector, i.e., L-Infinity norm of a vector

Scaled CVaR Norm

cvar_comp_abs

Average of the largest  (1-α)%  absolute values of components of a vector, where 0≤α≤1, i.e.,  Scaled CVaR  norm of a vector