Book:

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Ulrich Faigle, Walter Kern and Georg Still, "Algorithmic Principles of Mathematical Programming",
Kluwer Academic Publisher, 2002. (337 pages)

Contents

• Real Vector Spaces:
  Linear and Affine Space, Maps and Matrices, Inner Products and Norms, Continuous and Differentiable Functions
• Linear Equations and Linear Inequalities:
  Gaussian Elimination, Orthogonal Projection and Least Square Approximation, Integer Solutions of Linear Equations, Linear Inequalities
• Polyhedra:
  Polyhedral Cones and Polytopes, Cone Duality, Polar Duality of Convex Sets, Faces, Vertices and Polytopes, Rational Polyhedra
• Linear Programs and the Simplex Method:
  Linear Programs, The Simplex Method, Sensitivity Analysis, The Primal-Dual Simplex Method
• Lagrangian Duality:
  Lagrangian Relaxation, Lagrangian Duality, Cone Duality, Optimality Conditions
• An Interior Point Algorithm for Linear Programs:
  A Primal-Dual Relaxation, An Interior Point Method, Constructing Good Basic Solutions, Initialization and Rational Linear Programs, The Barrier Point of View
• Network Flows:
  Graphs, Shortest Paths, Maximum Flow, Min Cost Flows
• Complexity:
  Problems and Input Sizes, Algorithms and Running Times, Complexity of Problems, Arithmetic Complexity
• Integer Programming:
  Formulating an Integer Program, Cutting Planes I, Cutting Planes II, Branch and Bound, Lagrangian Relaxation, Dualizing the Binary Constraints
• Convex Sets and Convex Functions:
  Convex Sets, Convex Functions, Convex Minimization Problems, Quadratic Programming, The Ellipsoid Method, Applications of the Ellipsoid Method
• Unconstrained Optimization:
  Optimality Conditions, Descent Methods, Steepest Descent, Conjugate Directions, Line Search, Newton's Method,The Gauss-Newton Method, Quasi-Newton Methods, Minimization of Nondifferentiable Functions
• Constrained Nonlinear Optimization:
  First Order Optimality Conditions, Primal Methods,Second Order Optimality Conditions and Sensitivity, Penalty and Barrier Methods, Kuhn-Tucker Methods, Semi-infinite and Semidefinite Programs

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