Non linear programming

Mathematical Model and Optimization Non-Linear Programming (NLP) Model Decision Variables Objective (or Objective Function) Constraints Parameters Components of NLP Model  Non-Linear Programming(LP) Model: At least one non-linear term appears in either objective function or constraints Linear vs. Non-linear 2X1 + 3X2 2X12 + 3X1 2X1 + 3X1X2 2X1X2 2X1/X2 Linear Non-Linear Non-Linear Non-Linear Non-Linear Why Non-linear? Many business related events behaves non-linearly Examples) Yield curve of bonds: Term vs. Yield Revenue: Price X Quantity Marginal cost: Economy of Scale or Dis-economy of Scale As of 2011-August F(x,y)=-x^2 – y^2 F(x,y)= x^2 + y^2 Concave Function Convex Function Good structures for Non-linear Programming Non-linear Programming can be tricky to solve GRG is like Hill Climbing So, it will likely to End up at a local optima Neither convex Nor concave Ease of Optimization Reality of Model High Low High Low Linear Programming Non-Linear Programming minimize Based on data, estimate the relationship between hours and revenue. Y=aXb Based on data, estimate the relationship between hours and revenue. Y=a+b*log(X) Assignment Error measure 1: squared error Error measure 2: absolute error . constraints Linear vs. Non-linear 2X1 + 3X2 2X12 + 3X1 2X1 + 3X1X2 2X1X2 2X1/X2 Linear Non-Linear Non-Linear Non-Linear Non-Linear Why Non-linear? Many business related events behaves non-linearly Examples) Yield. Optimization Non-Linear Programming (NLP) Model Decision Variables Objective (or Objective Function) Constraints Parameters Components of NLP Model  Non-Linear Programming( LP) Model: At least one non-linear. 2011-August F(x,y)=-x^2 – y^2 F(x,y)= x^2 + y^2 Concave Function Convex Function Good structures for Non-linear Programming Non-linear Programming can be tricky to solve GRG is like Hill Climbing So, it will likely