Approximate directional stationarity is formulated as a necessary optimality condition for nonsmooth constrained problems, with a qualification condition using one sequence to infer directional stationarity.
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An inexact subgradient algorithm achieves O(ε^{-2}) iteration complexity for ε-accurate solutions to copositive programs while allowing inexact solves of NP-hard quadratic subproblems and providing a sufficient condition for non-complete positivity.
The paper characterizes Capra-convex sets and establishes that the ℓ0 pseudonorm equals its Capra-biconjugate, making ℓ0 Capra-convex.
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Approximate directional stationarity and associated qualification conditions
Approximate directional stationarity is formulated as a necessary optimality condition for nonsmooth constrained problems, with a qualification condition using one sequence to infer directional stationarity.
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Inexact subgradient algorithm with a non-asymptotic convergence guarantee for copositive programming problems
An inexact subgradient algorithm achieves O(ε^{-2}) iteration complexity for ε-accurate solutions to copositive programs while allowing inexact solves of NP-hard quadratic subproblems and providing a sufficient condition for non-complete positivity.
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What are Capra-Convex Sets?
The paper characterizes Capra-convex sets and establishes that the ℓ0 pseudonorm equals its Capra-biconjugate, making ℓ0 Capra-convex.