ABSTRACT
This chapter focuses on mathematical optimization. Mathematical optimization is the selection of a best element from some set of available alternatives. The most commonly used optimization algorithm in machine learning is the gradient descent. Many machine learning models can be solved by the gradient descent algorithm. The Lasso solution is very important in machine learning because of its sparsity, which results in the automated variable selection. There is a close relation between optimization and root-finding. Various root-finding methods are available in both R and Python. The chapter also focuses on an application of root-finding in finance, internal rate of return (IRR). IRR is a measure to estimate an investment’s potential profitability. In fact, it is a discount rate which makes the net present value of all future cashflows equal to zero. In linear programming (LP) both the objective function and the constraints are linear. Every LP problem falls into three categories: infeasible, unbounded, and having an optimal solution.
