Lecture 5

• Lecture 5
  • Physical Meaning of Lagrange Multipliers
  • Inequality constraints
  • Question
  • Numerical Method : Unconstrained prob
  • Steepest Descent
    • Stopping Criteria
    • Limitations
  • Momentum method
  • Variants
• we saw in last class Lagrange thing
  • converted equality constrained case to inconstrained thing
  • from where that was coming(formulae?)
• assume f is a function of 2 variables x1, and x2

• now moving from x1,x2 to x1+dx1, x2+dx2

then we equate dx2/dx1 from both the equations

Physical Meaning of Lagrange Multipliers

• a measure of how rigid constraints are
• say 2 constraints g1 and g2
• λ1, and λ2 are corresponding lagrange’s
• then larger λ => rigid constraint

Inequality constraints

• we add some slack variables
• Kuhn-tucker ne ineq constrained ko eq constrained me convert kardia

Question

• 1 eqns, 3 unknowns
• underdetermined system
• prob is
• find lagrangian, and partial derivatives
• answer is
• on matlab

Numerical Method : Unconstrained prob

Steepest Descent

Stopping Criteria

• so, 0.23 is optimum step size

• ans =

• if I start from black point, I end up at another minimum, which is not optimal
• I gpt stuck at local minimum

Limitations

Momentum method

Variants