## Abstract

We present a new result on the asymptotic behavior of nonautonomous subgradient evolution equations of the form u(t) ∈ - ∂o(u(t)), where {o_{t}: t ≥ 0} is a family of closed proper convex functions. The result is used to study the flow generated by the family o_{t}(x) = f(x, r(t)), where f(x, r) := c^{T}x + r ∑ exp[(A_{i}x-b_{i})/r] is the exponential penalty approximation of the linear program min {c^{T}x: Ax ≤ b}, and r(t) is a positive function tending to 0 when t → ∞. We prove that the trajectory u(t) converges to an optimal solution u^{∞} of the linear program, and we give conditions for the convergence of an associated dual trajectory μ(t) toward an optimal solution of the dual program.

Original language | English |
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Pages (from-to) | 263-273 |

Number of pages | 11 |

Journal | Journal of Functional Analysis |

Volume | 187 |

Issue number | 2 |

DOIs | |

State | Published - 20 Dec 2001 |

## Keywords

- Evolution equations
- Exponential penalty
- Linear programming