Optimization problem
In mathematics, 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:
- 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. They can include constrained problems and multimodal problems.
Continuous optimization problem
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The standard form of a continuous optimization problem is[1]
where
- f : ℝn → ℝ is the objective function to be minimized over the n-variable vector x,
- gi(x) ≤ 0 are called inequality constraints
- hj(x) = 0 are called equality constraints, and
- m ≥ 0 and p ≥ 0.
If m = p = 0, the problem is an unconstrained optimization problem. By convention, the standard form defines a minimization problem. A maximization problem can be treated by negating the objective function.
Combinatorial optimization problem
Formally, a combinatorial optimization problem A is a quadruple[citation needed] (I, f, m, g), where
- I is a set of instances;
- given an ins
See also
- Counting problem (complexity)
- Design Optimization
- Function problem
- Glove problem
- Operations research
- Satisficing: the optimum need not be found, just a "good enough" solution.
- Search problem
- Semi-infinite programming
References
- ^ Boyd, Stephen P.; Vandenberghe, Lieven (2004). Convex Optimization (pdf). Cambridge University Press. p. 129. ISBN 978-0-521-83378-3.
External links
- "How Traffic Shaping Optimizes Network Bandwidth". IPC. 12 July 2016. Retrieved 13 February 2017.
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