Linear Optimization and Approximation: An Introduction to the Theoretical Analysis and Numerical Trealment Of...
Weak duality; Applications of weak duality in uniform approximation; Duality theory; The simplex algorithm; Numerical realization of the simplex algorithm; A general three-phase algorithm; Approximation problems by chebyshev systems; Examples and applications of semi-infinite programming; References; Index.
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APPLICATIONS OF WEAK DUALITY IN UNIFORM
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applications approximation problem assume assumptions basic set calculated CC(A Chapter column vectors computational scheme Consider constraints construct Conv convex cone convex set corresponding defined denote described determine discretized problem dual pair dual preference function dual problem duality theorem elements error function Example exchange step Exercise extended Chebyshev system feasible vectors function f Gaussian Gaussian elimination given grid Hence index set inequalities interval linear combination linear optimization problem linear program linear system linearly independent lower bound mass-points mathematical matrix Maximize Minimize c y subject n-l n-l n+l n+l nonempty nonlinear system optimal basic solution optimal solution optimal value Phase points polynomial of degree primal Proof r=l r r real numbers representation result satisfy sequence simplex algorithm Slater condition solvable solved supporting hyperplane system of equations theory tion uniform approximation uniform norm unique solution vectors a(s verify yn+l zeros