A Relaxation of a Min-Cut Problem in an Anisotropic Continuous Network

Journal Article · Fri Jan 15 00:00:00 EST 1999 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S002459900113· OSTI ID:21067547

Nozawa, R. ^[1]

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1. School of Medicine, Sapporo Medical University, Sapporo, 060-8556 (Japan), E-mail: [e-mail]

Strang [18] introduced optimization problems on a Euclidean domain which are closely related with problems in mechanics and noted that the problems are regarded as continuous versions of famous max-flow and min-cut problems. In [15] we generalized the problems and called the generalized problems max-flow and min-cut problems of Strang's type. In this paper we formulate a relaxed version of the min-cut problem of Strang's type and prove the existence of optimal solutions under some suitable conditions. The conditions are essential. In fact, there is an example of the relaxed version which has no optimal solutions if the conditions are not fulfilled. We give such an example in the final section.

• OSTI ID: 21067547
• Journal Information: Applied Mathematics and Optimization, Vol. 40, Issue 1; Other Information: DOI: 10.1007/s002459900113; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANISOTROPY
EUCLIDEAN SPACE
MATHEMATICAL SOLUTIONS
MECHANICS
OPTIMIZATION
RELAXATION