TY - JOUR

T1 - DISCONTINUOUS OPTIMIZATION BY SMOOTHING.

AU - Zang, Israel

PY - 1981

Y1 - 1981

N2 - A tool is presented for solving many discontinuous optimization problems. The basic idea is to express discontinuities by means of a step function, and then to approximate the step function by a smooth one. This way, a smooth once or twice continuously differentiable approximate problem is obtained. This problem can be solved by any gradient technique. The approximations introduced contain a single parameter, which controls their accuracy so that the original problem is replaced only in some neighborhoods of the points of discontinuity. Some convergence properties are established, and numerical experiments with some test problems are reported.

AB - A tool is presented for solving many discontinuous optimization problems. The basic idea is to express discontinuities by means of a step function, and then to approximate the step function by a smooth one. This way, a smooth once or twice continuously differentiable approximate problem is obtained. This problem can be solved by any gradient technique. The approximations introduced contain a single parameter, which controls their accuracy so that the original problem is replaced only in some neighborhoods of the points of discontinuity. Some convergence properties are established, and numerical experiments with some test problems are reported.

UR - http://www.scopus.com/inward/record.url?scp=0019526061&partnerID=8YFLogxK

U2 - 10.1287/moor.6.1.140

DO - 10.1287/moor.6.1.140

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AN - SCOPUS:0019526061

SN - 0364-765X

VL - 6

SP - 140

EP - 152

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

IS - 1

ER -