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Rough Stability of Solutions to Nonconvex Optimization Problems

  • Hoang Xuan Phu
  • Hans Georg Bock
  • Sabine Pickenhain

Summary

The optimal solution set M(t) to some parametric optimization problem
$$\begin{array}{*{20}{c}} {minimize f(t,x)} & {subject to x \in D(t)} \\ \end{array}$$
is said to be roughly stable w.r.t. the roughness degree r > 0 at \( \bar t \in T\) if for all > 0 there is a neighborhood \( V\left( {\bar t} \right) \subset T\) of \( \bar t\) such that \( \left( {{ \cup _{t \in V\left( {\bar t} \right)}}M\left( t \right)} \right) < r + \in \) diam This paper states some sufficient conditions for this kind of generalized stability. One of the most important assumptions is that f is strictly roughly convexlike w.r.t. the roughness degree r. The result is applied to some optimal control problems, in particular, to a shipping problem.

Keywords

Optimal Control Problem Transportation Cost Neighborhood Versus Shipping Problem Linear Normed Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hoang Xuan Phu
    • 1
  • Hans Georg Bock
    • 2
  • Sabine Pickenhain
    • 3
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.IWR, University of HeidelbergHeidelbergGermany
  3. 3.Department of MathematicsTechnical University of CottbusCottbusGermany

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