--- title: Optimization description: Optimization is the study of finding the best solution to a problem given a set of constraints. Learners will understand how to formulate and solve linear, non-linear, and integer programming problems using various mathematical algorithms. category: mathematics subcategory: applied-mathematics difficulty: beginner, intermediate, advanced url: /subject/optimization --- # Optimization Optimization is the study of finding the best solution to a problem given a set of constraints. Learners will understand how to formulate and solve linear, non-linear, and integer programming problems using various mathematical algorithms. ## Available Resources 7 Books • 2 Courses ## Courses ### 1. Principles of Optimal Control (MIT 16.323) **Author:** Jonathan P. How Deterministic and stochastic optimal control for discrete and continuous systems, covering numerical search, dynamic programming, calculus of variations, Pontryagin's maximum principle and model predictive control. Provides detailed lecture notes, problem sets, exams and programming assignments for designing optimal controllers. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/16-323-principles-of-optimal-control-spring-2008/ **Tags:** optimal-control, dynamic-programming, model-predictive-control, calculus-of-variations, pontryagin-maximum-principle ### 2. Optimization Methods (MIT 15.093J) **Author:** Dimitris Bertsimas Graduate survey of optimization algorithms: the simplex method, network flows, branch and bound and cutting planes, nonlinear optimality conditions, interior point methods, Newton's method, and dynamic programming. Provides lecture notes, problem sets and exams, emphasizing the mathematical structure behind each method. **Difficulty:** Advanced | **Price:** Free **Link:** https://ocw.mit.edu/courses/15-093j-optimization-methods-fall-2009/ **Tags:** linear-programming, simplex-method, integer-programming, nonlinear-optimization, interior-point-methods, dynamic-programming ## Books ### 1. Hands-On Mathematical Optimization with Python **Author:** Krzysztof Postek, Alessandro Zocca, Joaquim Gromicho, Jeffrey Kantor Practical modeling textbook with Jupyter notebooks that formulate and solve linear, mixed-integer, network, convex/conic, robust and stochastic optimization problems in Pyomo with open-source solvers such as HiGHS. earners turn real problems into LP/MIP models and solve them with free tools before taking on the theory-heavy texts. Full content is free online. **Difficulty:** Beginner | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1009493507?tag=edmonddante07-20 **Tags:** mathematical-optimization, linear-programming, mixed-integer-programming, pyomo, python, operations-research ### 2. Algorithms for Optimization **Author:** Mykel J. Kochenderfer, Tim A. Wheeler Algorithm-focused textbook with runnable Julia code for every method: gradient and second-order descent, derivative-free and stochastic search, population methods, linear constrained optimization, surrogate models, multiobjective and uncertainty-aware design optimization. Official free PDF under CC BY-NC-ND. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0262039427?tag=edmonddante07-20 **Tags:** optimization-algorithms, gradient-descent, derivative-free-optimization, surrogate-models, julia, engineering-design ### 3. Integer Programming (2nd Edition) **Author:** Laurence A. Wolsey Compact textbook on optimization with discrete variables: formulations, LP relaxations and bounds, branch-and-bound, cutting planes, branch-and-cut, Lagrangian duality, column generation, Benders' decomposition, preprocessing and heuristics as used in modern MIP solvers. It is shorter and easier to approach than Nemhauser & Wolsey. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1119606535?tag=edmonddante07-20 **Tags:** integer-programming, branch-and-bound, cutting-planes, lagrangian-duality, decomposition, operations-research ### 4. Numerical Optimization (2nd Edition) **Author:** Jorge Nocedal, Stephen J. Wright Reference text on continuous nonlinear optimization algorithms: line search and trust-region methods, conjugate gradient, quasi-Newton (BFGS, L-BFGS), least squares, interior-point and SQP methods for constrained problems, and derivative-free optimization, with convergence analysis. Practitioners and research-group reading lists both point to it. It fills the 'how solvers actually work' gap that Boyd (theory and modeling) leaves. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0387303030?tag=edmonddante07-20 **Tags:** nonlinear-optimization, quasi-newton, trust-region, interior-point, sqp, numerical-methods ### 5. Introduction to Linear Optimization **Author:** Dimitris Bertsimas, John N. Tsitsiklis Graduate textbook on linear programming built on geometric intuition: the simplex method, duality, sensitivity analysis, network flows, interior-point methods, and an introduction to integer programming. The standard path into linear and discrete optimization. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1886529191?tag=edmonddante07-20 **Tags:** linear-programming, simplex-method, duality, network-flows, interior-point, operations-research ### 6. Convex Optimization **Author:** Stephen Boyd, Lieven Vandenberghe Comprehensive treatment of convex optimization theory and algorithms covering duality, approximation, statistical estimation, and geometric problems. **Difficulty:** Advanced | **Language:** English | **Price:** Free **Link:** https://web.stanford.edu/~boyd/cvxbook/ **Tags:** book, mathematics, applied-mathematics ### 7. Geometric Algorithms and Combinatorial Optimization **Author:** Martin Grötschel, László Lovász, Alexander Schrijver Research monograph showing how the ellipsoid method and lattice basis reduction yield polynomial-time algorithms for combinatorial optimization. Establishes the equivalence of separation and optimization over polyhedra, then applies it to matroids, submodular functions, perfect graphs and other structured problems. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/3540567402?tag=edmonddante07-20 **Tags:** combinatorial-optimization, ellipsoid-method, polyhedral-combinatorics, lattice-basis-reduction, linear-programming --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/optimization