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 PrimalDual Simplex Method

Lagrangian Duality:
Lagrangian Relaxation, Lagrangian Duality,
Cone Duality, Optimality Conditions

An Interior Point Algorithm for Linear Programs:
A PrimalDual 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 GaussNewton Method,
QuasiNewton Methods,
Minimization of Nondifferentiable Functions

Constrained Nonlinear Optimization:
First Order Optimality Conditions,
Primal Methods,Second Order Optimality Conditions and Sensitivity,
Penalty and Barrier Methods,
KuhnTucker Methods,
Semiinfinite and Semidefinite Programs
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