Non-Linear Optimization Flashcards
Concave function
A function that is bowl-shaped down
Convex function
A function that is bowl-shaped up.
Efficient frontier
A set of points defining the minimum possible risk (measured by portfolio variance) for a set of return values.
Global maximum
A feasible solution where there are no other feasible points with a larger objective function value in the entire feasible region.
Global minimum
A feasible solution where there are no other feasible points with a smaller objective function value in the entire feasible region.
global optimum
A feasible solution where there are no other feasible points with a better objective function value in the entire feasible region.
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.
Local maximum
A feasible solution where there are no other feasible solutions with a larger objective function value in the immediate neighborhood.
Local minimum
A feasible solution where there are no other feasible solutions with a smaller objective function value in the immediate neighborhood.
Local optimum
A feasible solution where there are no other feasible solutions with a better objective function value in the immediate neighborhood.
Markowitz mean-variance portfolio model
An optimization model used to construct a portfolio that minimizes risk subject to a constraint requiring a minimum level of return.
Nonlinear optimization problem
an optimization problem that contains at least one nonlinear term in the objective function or a constraint
Quadratic function
A nonlinear function with terms to the power of two
Reduced gradient
Value associated with a variable in a nonlinear model that is analogous to the reduced cost in a linear model; the shadow price of a binding simple lower or upper bound on the decision variable.
