"Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships.
en.wikipedia.org › wiki › Linear_programming
Linear programming - Wikipedia
"Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm."
https://en.wikipedia.org/wiki/Branch_and_bound
Convex Optimization Branch and Bound Methods
https://people.orie.cornell.edu/mru8/orie6326/lectures/sp.pdf
Semidefinite Programming and Max-Cut
https://www.cs.cmu.edu/~anupamg/adv-approx/lecture14.pdf
Relating max-cut problems and binary linear feasibility problems
http://www.optimization-online.org/DB_FILE/2009/02/2237.pdf
"Branch and cut[1] is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values.[2] Branch and cut involves running a branch and bound algorithm and using cutting planes to tighten the linear programming relaxations. Note that if cuts are only used to tighten the initial LP relaxation, the algorithm is called cut and branch."
https://en.wikipedia.org/wiki/Branch_and_cut
Integer Programming
http://web.mit.edu/15.053/www/AMP-Chapter-09.pdf
Bang–bang solutions in optimal control
"In optimal control problems, it is sometimes the case that a control is restricted to be between a lower and an upper bound. If the optimal control switches from one extreme to the other (i.e., is strictly never in between the bounds), then that control is referred to as a bang-bang solution.
Bang–bang controls frequently arise in minimum-time problems. For example, if it is desired to stop a car in the shortest possible time at a certain position ahead of the car, the solution is to apply maximum acceleration until the unique switching point, and then apply maximum braking to come to rest exactly at the desired position."
https://en.wikipedia.org/wiki/Bang%E2%80%93bang_control
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Sayed Ahmed
BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
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