Applied Optimization: Linear, Nonlinear, & ML Focus

Compare human learning and machine learning. Find how materials and data drive learning, and how optimization updates model parameters to solve real problems.

Explore implementing linear optimization in Matlab using the leapfrog method to maximize profit in a chocolate production case, converting to a minimization problem and solving with dual simplex.

Apply Matlab to solve a linear optimization problem for the agriculture case study two, allocating land between wheat and barley on 100 hectares to maximize profit.

Explore constrained nonlinear optimization by forming the Lagrange equation, taking partial derivatives with respect to x, y, and lambda, and solving for x, y, lambda to minimize f(x,y) under g(x,y)=0.

Derive economic load dispatch for a two-generator plant using the lagrange multiplier method to minimize cost under the constraint p1 + p2 = PD, deriving p1 and p2 from lambda.

Apply the Lagrange multiplier method in MATLAB to solve a constrained nonlinear optimization for a three-generator power plant, determining lambda and generator outputs to meet 800 MW at minimum cost.

Explore unconstrained nonlinear optimization through the gradient descent algorithm, detailing gradient, learning rate, step length, and convergence criteria for convex or concave objective functions.

Apply gradient descent to single-variable nonlinear unconstrained optimization in Matlab. Randomly initialize x, compute gradient 2x, update x by delta x = -eta*gradient, and iterate to reach x=0, f(x)=5.

Apply Python gradient descent to minimize f(x)=x^2+5 by initializing x and a learning rate, iterating to update x with delta x = -eta * 2x, converging to x=0 and f(0)=5.

Explore multivariable nonlinear unconstrained optimization using gradient descent to minimize f(x,y)=x^2+y^2+10, initializing variables and learning rate, computing gradients, and updating x and y over epochs.

Apply gradient descent algorithm to a multivariable non-linear unconstrained optimization problem. The video demonstrates minimizing f(x,y)=x^2+y^2+10 with random initialization, learning rate 0.1, and two epochs, detailing gradients and updates.

Explore multivariable nonlinear optimization with gradient descent in python on google colab, starting from random x and y, tuning learning rate and epochs to minimize f=3x^2+5y^2+10.

Learn how optimization underpins machine learning, from linear and nonlinear problems to gradient descent, with case studies and the role of optimization in improving ML models.