Titlebook: Optimization on Low Rank Nonconvex Structures; Hiroshi Konno,Phan Thien Thach,Hoang Tuy Book 1997 Springer Science+Business Media Dordrech

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Continuous LocationLow rank nonconvex problems occur in many practical applications. In this chapter we discuss problems of continuous location which are highly nonconvex by their geometric nature, however can often be efficiently solved due to the low dimensionality of the underlying space.

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1571-568X t deterministic algorithms have been proposed in the last tenyears for solving several classes of large scale specially structuredproblems encountered in such areas as chemical engineering, financialengineering, location and network optimization, production andinventory control, engineering design,

locus-ceruleus

harmony

积极词汇

D.C. Functions and D.C. Setsructure makes it a very convenient framework for a unified approach to an extremely broad class of problems at first sight very different from each other. For the design of efficient solution methods for these problems, it is, therefore, necessary to understand the d.c. structure.

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Low-Rank Nonconvex Structures integer linear programming problems were developed in the 60’s (Benders (1962), Rosen (1964), Ritter (1967)) and ever since extended to nonlinear programming with many applications (Balas (1970), Geoffrion (1970), (1972)), Fleischmann (1973), Tind and Wolsey (1981), Burkard et al. (1985), Tuy (1987).

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Global Search Methods and Basic D.C. Optimization Algorithmsoblem of this class into a sequence of subproblems of low dimension, whose data are adaptively generated from those of the original problem. These subproblems of low dimension are often solved by a specialized version of some general purpose method.

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Low Rank Nonconvex Quadratic Programmingen successfully applied to a number of practical problems in portfolio analysis (Pang (1980), Takehara (1993), etc.. Also it has been used as a sub-procedure for solving general convex minimization problems (Boggs and Tolle (1995)).