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Optimization problems arise in all quantitative disciplines from computer science and engineering [3] to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. [4] [5]
In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete :
Combinatorial optimization is related to operations research, algorithm theory, and computational complexity theory. It has important applications in several fields, including artificial intelligence, machine learning, auction theory, software engineering, VLSI, applied mathematics and theoretical computer science.
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 and objective are represented by linear relationships.
If sub-problems can be nested recursively inside larger problems, so that dynamic programming methods are applicable, then there is a relation between the value of the larger problem and the values of the sub-problems. [1] In the optimization literature this relationship is called the Bellman equation.
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization , some or all of the variables used in a discrete optimization problem are restricted to be discrete variables —that is, to assume only a discrete set of values, such as the integers .
For example, one of the long-standing open questions in computer science is to determine whether there is an algorithm that outperforms the 2-approximation for the Steiner Forest problem by Agrawal et al. [3] The desire to understand hard optimization problems from the perspective of approximability is motivated by the discovery of surprising ...
Genetic improvement (computer science) Golden-section search; Gradient descent; Gradient method; Graduated optimization; Great deluge algorithm; Greedy algorithm; Greedy triangulation; Guided local search; Guillotine cutting; Guillotine partition