Book on Mathematical Optimisation

Question

I need a book on mathematical optimisation which covers as many topics from the following list as possible:

• Introduction (Graphs, Paths, Network Planning, Spanning Trees, Matchings),
• Matroids (Independence Systems and Matroids, Bases, Circuits and Ranks, Maximization over Independence Systems and Matroids Minimization over Bases Systems)
• Running Time of Algorithms (Algorithms, Encoding Length, Polynomial-time Algorithms, first Polynomial-time Computations),
• Dynamic Programming (Multilevel Decision Processes, Knapsack Problem, Shortest Walks and Paths),
• Optimization in Networks (Flows and Cuts, Augmentation, Algorithm of Dinic),
• Elements of Complexity Theory

It would also be helpful if you could tell me the prerequisite background for the same.

Answer 1

I don’t know the books that would cover everything, but I can suggest one good book and one review through which you can find other useful sources. Hope this helps.

Multilevel decision-making: A survey

Multilevel Optimization: Algorithms and Applications

Answer 2

The book Combinatorial Optimization: Algorithms and Complexity by Papadimitriou and Steiglitz covers much of what you require. It is a little bit dated perhaps (written in 1982) but well-written and pretty comprehensive.