1995

# LGO : an implementation of a Lipschitzian global optimization procedure

## Publication

### Publication

Decision problems are frequently modelled by optimizing the value of a primary objective function under stated feasibility constraints. Specifically, we shall consider here the following global optimization problem: begin{equation min f(x) mbox{ subject to x in D subset RR^n . end{equation We shall assume that in (GOP) $f:D rightarrow RR$ is a continuous function, and D is a bounded, robust subset (`body') in the Euclidean n-space. In addition, the Lipschitz-continuity of f on D will also be postulated, when necessary. The above assumptions define a fairly general class of optimization problems, and typically reflect a paradigm in which a rather vaguely defined, `large' search region is given on which a (potentially) multiextremal function f is minimized. It will also be assumed that the set of global solutions $X^* subset D$ is, at most, countable. To solve (GOP), a general family of adaptive partition strategies can be introduced: consult Pintér (1992a, 1995) and references therein. Necessary and sufficient convergence conditions can be established: these lead to a unified view of numerous GO algorithms, permitting their straightforward generalization and various extensions to handle specific cases of (GOP). The present report discusses a Lipschitzian global optimization program system, for use in the workstation environment at CWI. Implementation aspects are detailed, numerical experience, existing and prospective applications are also highlighted. Application areas include, e.g., the following (Pintér, 1992b, 1995): general (Lipschitzian) nonlinear approximation, systems of nonlinear equations and inequalities, calibration (parameterization) of descriptive system models, data classification, general configuration design, aggregation of negotiated expert opinions, product/mixture design, `black box' design and operation of engineering/environmental systems.

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CWI | |

Department of Numerical Mathematics [NM] | |

Pintér, J.D. (1995).
LGO : an implementation of a Lipschitzian global optimization procedure. Department of Numerical Mathematics [NM]. CWI. |