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Discontinuous piecewise differentiable optimization I : theory

Abstract : A theoretical framework and a practical algorithm are presented to solve discontinuous piecewise linear optimization problems. A penalty approach allows one to consider such problems subject to a wide range of constraints involving piecewise linear functions. Although the theory is expounded in detail in the special case of discontinuous piecewise linear functions, it is straightforwardly extendable, using standard non linear programming techniques, to the nonlinear (discontinuous piecewise differentiable) situation to yield a first order algorithm. This work is presented in two parts. We introduce the theory in this first paper. The descent algorithm which is elaborated uses active set and projected gradient approaches. It is generalization of the ideas used by Conn to deal with nonsmoothness in the l1 exact penalty function, and it is based on the notion of decomposition of a function into a smooth and a nonsmooth part. In an accompanying paper, we shall tackle constraints via a penalty approach, we shall discuss the degenerate situation, the implementation of the algorithm, and numerical results will be presented.
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Submitted on : Monday, May 29, 2006 - 11:38:06 AM
Last modification on : Friday, February 4, 2022 - 3:13:45 AM
Long-term archiving on: : Friday, May 13, 2011 - 10:06:09 PM


  • HAL Id : inria-00076929, version 1



A.R. Conn, Marcel Mongeau. Discontinuous piecewise differentiable optimization I : theory. [Research Report] RR-1694, INRIA. 1992. ⟨inria-00076929⟩



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