Downloads¶
The lecture notes and the exercise books in PDF, updated at every publication of the site, with the same numbering of definitions, theorems, examples and exercises as the website. Text and figures are released under CC BY 4.0.
Lecture notes¶
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Lecture notes, volume 1 · Linear functions, polyhedra and linear programming problems
Linear functions (gradient, Hessian and level sets), half-spaces and polyhedra, linear optimization problems with their optimal solutions, examples and properties, the canonical and standard forms with the graphical method, possible outcomes and equivalences between forms.
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Lecture notes, volume 2 · The simplex algorithm
The simplex algorithm on dictionaries, optimality conditions, pivot rules and cycling, Phase 0 with the auxiliary problem. Examples worked out step by step and exercises with complete solutions at the end of each chapter.
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Lecture notes, volume 3 · Duality and the dual simplex
The dual problem, weak and strong duality, the possible outcomes of a primal-dual pair, complementary slackness; the dual simplex algorithm, infeasibility certificates and re-optimization. Examples worked out step by step and exercises with complete solutions at the end of each chapter.
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Lecture notes, volume 4 · Matrix methods, sensitivity and geometry
The revised primal and dual simplex, the primal-dual method, sensitivity analysis, the geometry of linear programming (faces, vertices and basic solutions). Examples worked out step by step and exercises with complete solutions at the end of each chapter.
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Lecture notes, volume 5 · Modelling
Techniques for writing a linear programming model from the description of a problem (production, blending, transportation, multi-period planning, linearizations), with worked examples. Complete models are in Exercises 5.
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Problem catalogue · Catalogue of LP problems
The linear programming problems used in the examples and exercises of the whole course, cited by their code P0--P86: problems with two and three variables, in four types (A: non-negative right-hand sides; B: dual simplex; C: Phase 0 needed; D: unbounded, infeasible or with multiple optima). For each, the problem and the figure of its feasible region.
Exercises¶
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Exercises, volume 1 · Linear functions, polyhedra and linear programming problems
Worked exercises on half-spaces and polyhedra, linear optimization problems in one variable, the graphical method and equivalences.
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Exercises, volume 2 · The simplex algorithm
Worked exercises on chapters 6--8: dictionaries, the simplex algorithm, cycling and Bland's rule, Phase 0. Each exercise uses a problem of the catalogue and has a complete solution.
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Exercises, volume 3 · Duality and the dual simplex
Worked exercises on chapters 9--10: building the dual, graphical solution of primal and dual, complementary slackness, primal-dual outcomes, the dual simplex algorithm.
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Exercises, volume 4 · Matrix methods, sensitivity and geometry
Worked exercises on chapters 11--15: revised primal and dual simplex, primal-dual method, sensitivity analysis, geometry of linear programming.
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Exercises, volume 5 · Linear programming models
Worked linear programming models: symbolic models with their instance, a feasible solution and a dual bound, and numerical models.