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between two points in a plane. The variables in this problem are the curves connecting the two points. The optimal solution is of course the line segment joining the points, if the metric defined on the plane is the
Euclidean
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Given two cities in a country with many hills and valleys, find the shortest road going from one city to the other. This problem is a generalization of the above, and the solution is not as obvious.
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Given two circles which will serve as top and bottom for a cup of given height, find the shape of the side wall of the cup so that the side wall has
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Infinite-dimensional optimization problems can be more challenging than finite-dimensional ones. Typically one needs to employ methods from
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problems the unknown optimal solution might not be a number or a vector, but rather a continuous quantity, for example a
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Cassel, Kevin W.: Variational
Methods with Applications in Science and Engineering, Cambridge University Press, 2013.
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Find the shape of a bridge capable of sustaining given amount of traffic using the smallest amount of material.
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Several disciplines which study infinite-dimensional optimization problems are
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problem, because, a continuous quantity cannot be determined by a
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24:or the shape of a body. Such a problem is an
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116:Optimization by Vector Space Methods.
129:Edward J. Anderson and Peter Nash,
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229:Infinite-dimensional optimization
138:Linear Semi-Infinite Optimization
26:infinite-dimensional optimization
178:Major subfields of optimization
136:M. A. Goberna and M. A. López,
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78:to solve such problems.
239:Constraint satisfaction
214:Stochastic programming
194:Fractional programming
83:calculus of variations
209:Nonlinear programming
204:Quadratic programming
270:Functional analysis
249:Simulated annealing
219:Robust optimization
199:Integer programming
189:Convex programming
91:shape optimization
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40:Examples
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50:metric.
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