Infinite-dimensional optimization

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In certain optimization problems the unknown optimal solution might not be a number or a vector, but rather a continuous quantity, for example a function or the shape of a body. Such a problem is an infinite-dimensional optimization problem, because, a continuous quantity cannot be determined by a finite number of certain degrees of freedom.

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Examples

Infinite-dimensional optimization problems can be more challenging than finite-dimensional ones. Typically one needs to employ methods from partial differential equations to solve such problems.

Several disciplines which study infinite-dimensional optimization problems are calculus of variations, optimal control and shape optimization.

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