Non linear programming

Mathematical Model and Optimization Non-Linear Programming NLP Model... Decision VariablesObjective or Objective Function Constraints Parameters Components of NLP Model  Non-Linear Pro

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

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

Portfolio Optimization using the Markowitz Model

C: Covariance Matrix of Stocks (n by n)