Ch. 10 terms

Global optimum

a feasible solution if there are no other feasible points with a better objective function value in the entire feasible region. can either be global max or min.

Global maximum

a feasible solution if there are no other feasible points with a larger objective function value in the entire feasible region.

Global minimum

a feasible solution if there are no other feasible points with a smaller objective function value in the entire feasible region.

Local optimum

a feasible solution if there are no other feasible solutions with a better objective function value in the immediate neighborhood. can either be local max or local min.

Local Maximum

a feasible solution if there are no other feasible solutions with a larger objective function value in the immediate neighborhood

Local minimum

a feasible solution if there are no other feasible solutions with a smaller objective function value in the immediate neighborhood

concave function

a function that is bowl-shaped down

convex function

a function that is bowl-shaped up

quadratic function

a nonlinear function with term to the power two

Markowitz mean-variance portfolio model

a portfolio optimization model used to construct a portfolio that minimizes risk subject to a constraint requiring a minimum level of return

efficient frontier

a set of points defining the minimum possible risk for a set of return values

nonlinear optimization problem

an optimization problem that contains at least one nonlinear term in the objective function or a constraint

lagrangian multiplier

the shadow price for a constraint in a nonlinear problem that is the rate of change of the objective function with respect to the right hand side of a constraint

reduced gradient

value associated with a variable in a nonlinear model that is analogous to the reduced cost in a linear model