Reference book for these types of problems

Question

From time to time I come across problems similar to (min, max, max min, etc)

\begin{equation} \begin{aligned} \min_{j,i} \quad & (j-i)\\ \textrm{s.t.} \quad & i \le j\\ & n \ge i,j \ge 0 \\ & \textrm{some nonlinear/combinatorial conditions} \\ \end{aligned} \end{equation}

and I know I can change it to

\begin{equation} \begin{aligned} \min_{j} \quad (j- &\max_{i} i)\\ & \textrm{s.t.} \quad n \ge j \ge i \ge 0 \\ & \textrm{some nonlinear/combinatorial conditions} \\ \end{aligned} \end{equation}

and come up with an algorithm to solve it by iterating over j. Can you please tell me if there is a book in which these rules of separation, associative/commutative/etc, conversion of min to max or max to min, and more general principles are taught?

Answer 1

Most Linear Programming books cover topics like model conversion like you mentioned, though they tend to be sub-topics of often larger problems. If you’re looking to get into Linear and Non-Linear Programming (since you mentioned Non-Linear and combinatorial constraints):

• “Non-Linear Programming: Theory and Algorithms, 3rd Edition” by Mokhtar S. Bazaraa

• Hyper comprehensive book list of Linear/Integer/etc.

• A couple Non-Linear and Linear book references and some others

If you want general practice problems:

• Problems in OR and e.t.c.

• The practice problems that appear dynamically by Google