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  • 1
    Electronic Resource
    Electronic Resource
    Presolving in linear programming (1995)
    Springer
    Mathematical programming 71 (1995), S. 221-245 
    Details
    ISSN: 1436-4646
    Keywords: Linear programming ; Presolving ; Interior-point methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Most modern linear programming solvers analyze the LP problem before submitting it to optimization. Some examples are the solvers WHIZARD (Tomlin and Welch, 1983), OB1 (Lustig et al., 1994), OSL (Forrest and Tomlin, 1992), Sciconic (1990) and CPLEX (Bixby, 1994). The purpose of the presolve phase is to reduce the problem size and to discover whether the problem is unbounded or infeasible. In this paper we present a comprehensive survey of presolve methods. Moreover, we discuss the restoration procedure in detail, i.e., the procedure that undoes the presolve. Computational results on the NETLIB problems (Gay, 1985) are reported to illustrate the efficiency of the presolve methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586000
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  • 2
    Electronic Resource
    Electronic Resource
    Minimizing a Sum of Norms Subject to Linear Equality Constraints (1998)
    Springer
    Computational optimization and applications 11 (1998), S. 65-79 
    Details
    ISSN: 1573-2894
    Keywords: sum of norms ; non-smooth optimization ; duality ; Newton barrier method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Numerical analysis of a class of nonlinear duality problems is presented. One side of the duality is to minimize a sum of Euclidean norms subject to linear equality constraints (the constrained MSN problem). The other side is to maximize a linear objective function subject to homogeneous linear equality constraints and quadratic inequalities. Large sparse problems of this form result from the discretization of infinite dimensional duality problems in plastic collapse analysis. The solution method is based on the l 1 penalty function approach to the constrained MSN problem. This can be formulated as an unconstrained MSN problem for which the first author has recently published an efficient Newton barrier method, and for which new methods are still being developed. Numerical results are presented for plastic collapse problems with up to 180000 variables, 90000 terms in the sum of norms and 90000 linear constraints. The obtained accuracy is of order 10-8 measured in feasibility and duality gap.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018322318259
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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