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An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found.
Design optimization applies the methods of mathematical optimization to design problem formulations and it is sometimes used interchangeably with the term engineering optimization. When the objective function f is a vector rather than a scalar , the problem becomes a multi-objective optimization one.
In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover" [1]) is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution in a search space.
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.
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.
Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. [6] The method is largely due to the work of Lev Pontryagin and Richard Bellman in the 1950s, after contributions to calculus of variations by Edward J. McShane . [ 7 ]
Engineering optimization [1] [2] [3] is the subject which uses optimization techniques to achieve design goals in engineering. [ 4 ] [ 5 ] It is sometimes referred to as design optimization . Topics
Optimization comes at a price and it is important to be sure that the investment is worthwhile. An automatic optimizer (or optimizing compiler, a program that performs code optimization) may itself have to be optimized, either to further improve the efficiency of its target programs or else speed up its own operation. A compilation performed ...