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Adrian Lewis

Two Numerical Methods for Optimizing Matrix Stability

Published: 2001/05/31
  • James V. Burke
  • Adrian Lewis
  • Michael L. Overton
  • Categories Nonsmooth Optimization

    Consider the affine matrix family $A(x) = A_0 + \sum_{k=1}^m x_k A_k$, mapping a design vector $x\in\Rl^m$ into the space of $n \times n$ real matrices. Consider the affine matrix family $A(x) = A_0 + \sum_{k=1}^m x_k A_k$, mapping a design vector $x\in\Rl^m$ into the space of $n \times n$ real matrices. We are interested … Read more

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    Keywords

    alternating direction method of multipliers augmented lagrangian method benders decomposition bilevel optimization Branch-and-Bound branch-and-cut chance constraints column generation combinatorial optimization complexity convergence rate 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 multiobjective optimization 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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