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dikin’s ellipsoid

The Legendre Transformation in Modern Optimization

Published: 2016/01/17
  • Roman Polyak
  • Categories Constrained Nonlinear Optimization, Convex Optimization Tags dikin's ellipsoid

    The Legendre transformation (LET) is a product of a general duality principle: any smooth curve is, on the one hand, a locus of pairs, which satisfy the given equation and, on the other hand, an envelope of a family of its tangent lines. Application of LET to a strictly convex and smooth function leads to … Read more

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    Keywords

    alternating direction method of multipliers approximation algorithms augmented lagrangian method bilevel optimization Branch-and-Bound branch-and-cut chance constraints column generation combinatorial optimization complexity compressed sensing conic optimization convex optimization cutting planes decomposition derivative-free optimization distributionally robust optimization duality dynamic programming first-order methods global convergence global optimization heuristics integer programming interior point methods large-scale optimization linear programming machine learning mixed-integer linear programming mixed-integer nonlinear programming mixed-integer programming nonconvex optimization nonlinear optimization nonlinear programming nonsmooth optimization optimal control optimization proximal point algorithm quadratic programming robust optimization semidefinite programming stochastic optimization stochastic programming trust-region methods unconstrained optimization

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