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Reference.org
Lagrange multipliers on Banach spaces
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<p>In the field of <a href="/facts/Calculus_of_variations/Ya5Lsma3">calculus of variations</a> in <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the method of Lagrange multipliers on Banach spaces can be used to solve certain infinite-dimensional <a href="/facts/Constraint_(mathematics)/QLFIFlFX">constrained</a> <a href="/facts/Optimization_(mathematics)/oRn8Iv5I">optimization problems</a>. The method is a generalization of the classical method of <a href="/facts/Lagrange_multipliers/U5mSI5YP">Lagrange multipliers</a> as used to find <a href="/facts/Extremum/ADlgnyzV">extrema</a> of a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> of finitely many variables. </p>