Stationary Point Definition of stationary point from wikipedia : In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally, it is a point where the function "stops" increasing or decreasing… Continue reading Lagrange Multiplier With Equality Constraints

# Tag: optimization

# Lagrange Duality

There are three things : Original problem (Primal problem) Dual function (Function of lagrange multiplier) Dual problem Suppose p is the solution of primal problem and d the dual problem. If original problem is minimization, we are interested in lower bound (d) such that d<p. We want to find maximum value of d… Continue reading Lagrange Duality

# Lagrange Multiplier and Constrained Optimization

Lagrange multipliers helps us to solve constrained optimization problem. An example would to maximize f(x, y) with the constraint of g(x, y) = 0. Geometrical intuition is that points on g where f either maximizes or minimizes would be will have a parallel gradient of f and g ∇ f(x, y) = λ ∇ g(x,… Continue reading Lagrange Multiplier and Constrained Optimization