The text is divided into three main parts: unconstrained optimization, constrained optimization, and linear programming. The first part addresses unconstrained optimization in single-variable and multivariable functions, introducing key algorithms such as steepest descent, Newton, and quasi-Newton methods.
The second part focuses on constrained optimization, starting with linear equality constraints and extending to more general cases, including inequality constraints. It details optimality conditions, sensitivity analysis, and relevant algorithms for solving these problems.
The third part covers linear programming, presenting the formulation of LP problems, the simplex algorithm, and sensitivity analysis. Throughout, the text provides numerous applications to data science, such as linear regression, maximum likelihood estimation, expectation-maximization algorithms, support vector machines, and linear neural networks.
Contents:
- Unconstrained Optimization:
- Single-Variable Optimization
- Multi-Variable Unconstrained Optimization
- Constrained Optimization:
- Optimization Under Equality Constraints: Special Cases
- Optimization Under Equality Constraints: The General Case
- Optimization Under Equality and Inequality Constraints
- Linear Programming:
- Introduction and Examples
- The Simplex Method
- Sensitivity Analysis
- Solutions to Exercises
Readership: Third-year undergraduates and above, as well as Master's and PhD students in data science, statistics, computer science, engineering, operations research, mathematics, and economics.
