LinearFractionalOptimization

LinearFractionalOptimization[f, cons, vars] finds values of variables vars that minimize the linear fractional objective f subject to linear constraints cons.

• LinearFractionalOptimization[{α, β, γ, δ}, {a, b}] finds a vector x that minimizes the linear fractional function (α.x+β)/(γ.x+δ) subject to the linear inequality constraints a.x+b⪰0.
• LinearFractionalOptimization[{α, β, γ, δ}, {a, b}, {aeq, beq}] includes the linear equality constraints aeq.x+beq=0.
• LinearFractionalOptimization[{α, β, γ, δ}, ..., {dom1, dom2, ...}] takes xi to be in the domain domi, where domi is Integers or Reals.
• LinearFractionalOptimization[..., "prop"] specifies what solution property "prop" should be returned.

Examples

Minimize a linear fractional function:

LinearFractionalOptimization[(x + 1)/(2 x + 3), {x >= 0, x <= 10}, {x}]

With matrix constraints:

LinearFractionalOptimization[{c1, d1, c2, d2}, {A, b}]

Please visit the official Wolfram Language Reference for more details.