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**The complementary convex structure in global optimization.**
*(English)*
Zbl 0787.90091

Summary: We show the importance of exploiting the complementary convex structure for efficiently solving a wide class of specially structured nonconvex global optimization problems. Roughly speaking, a specific feature of these problems is that their nonconvex nucleus can be transformed into a complementary convex structure which can then be shifted to a subspace of much lower dimension than the original underlying space. This approach leads to quite efficient algorithms for many problems of practical interest, including linear and convex multiplicative programming problems, concave minimization problems with few nonlinear variables, bilevel linear optimization problems, etc...

### MSC:

90C30 | Nonlinear programming |

90-08 | Computational methods for problems pertaining to operations research and mathematical programming |

### Keywords:

generalized rank \(k\) property; specially structured nonconvex global optimization; nonconvex nucleus; complementary convex structure
Full Text:
DOI

### References:

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