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Bookmark or Share- Duality (mathematics) - WikipediaIn 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.
- Convex Optimization - Stanford UniversityLagrange dual function. Lagrange dual function: g : Rm × Rp → R, g(, ) = inf L(x, , x∈D. m p. ∑︁ ∑︁ ) = inf f0(x) + ifi(x) + ihi(x) x∈D i=1 i=1. g is concave, can be −∞ for some , lower bound property: if. ⪰ 0, then g(, ) ≤ p★ proof: if ̃x is feasible and. f0( ̃x) ≥ L( ̃x, , ) ≥ inf L(x, , ) = g(, )
- Lagrangian Duality for Dummies - Stanford University Computer Sciencewhere g( ) = minx L(x; ) is known as the dual function. Maximising the dual function g( ) is known as the dual problem, in the constrast the orig-inal primal problem. Since g( ) is a pointwise minimum of a ne functions (L(x; ) is a ne, i.e. linear, in ), it is a concave function.
- Lagrangean duality - Cornell University Computational Optimization Open ...The Lagrangean dual has become a common approach to solving optimization problems. Many problems can be efficiently solved by constructing the Lagrangean function of the problem and solving the dual problem instead of the primal problem.
- Duality Theory of Constrained Optimization - MIT OpenCourseWareConstructing the dual involves a three-step process: • Step 1. Create the Lagrangian L(x,u):=f (x)+uTg(x). • Step 2. Create the dual function: L∗(u) := minimum x f(x)+uT g(x) s.t. x ∈ X • Step 3. Create the dual problem: D: v ∗ =maximum u L∗(u) s.t. u ≥ 0
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