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  2. Strong duality - Wikipedia

    en.wikipedia.org/wiki/Strong_duality

    Strong duality is a condition in mathematical optimization in which the primal optimal objective and the dual optimal objective are equal. By definition, strong duality holds if and only if the duality gap is equal to 0.

  3. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    The max-flow min-cut theorem is a special case of the strong duality theorem: flow-maximization is the primal LP, and cut-minimization is the dual LP. See Max-flow min-cut theorem#Linear program formulation. Other graph-related theorems can be proved using the strong duality theorem, in particular, Konig's theorem. [9]

  4. Karush–Kuhn–Tucker conditions - Wikipedia

    en.wikipedia.org/wiki/Karush–Kuhn–Tucker...

    Theorem — (sufficiency) If there exists a solution to the primal problem, a solution (,) to the dual problem, such that together they satisfy the KKT conditions, then the problem pair has strong duality, and , (,) is a solution pair to the primal and dual problems.

  5. Duality (optimization) - Wikipedia

    en.wikipedia.org/wiki/Duality_(optimization)

    The duality gap is zero if and only if strong duality holds. Otherwise the gap is strictly positive and weak duality holds. [5] In computational optimization, another "duality gap" is often reported, which is the difference in value between any dual solution and the value of a feasible but suboptimal iterate for the primal problem.

  6. Fenchel–Moreau theorem - Wikipedia

    en.wikipedia.org/wiki/Fenchel–Moreau_theorem

    A function that is not lower semi-continuous.By the Fenchel-Moreau theorem, this function is not equal to its biconjugate.. In convex analysis, the Fenchel–Moreau theorem (named after Werner Fenchel and Jean Jacques Moreau) or Fenchel biconjugation theorem (or just biconjugation theorem) is a theorem which gives necessary and sufficient conditions for a function to be equal to its biconjugate.

  7. List of dualities - Wikipedia

    en.wikipedia.org/wiki/List_of_dualities

    In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A.

  8. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    Bolzano's theorem (real analysis, calculus) Bolzano–Weierstrass theorem (real analysis, calculus) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec theorem (number theory) Bondareva–Shapley theorem ; Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Bonnet theorem (differential geometry)

  9. Duality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Duality_(mathematics)

    In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A.

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