Mathematical programming via the least-squares method |
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Authors: | Evald Übi |
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Institution: | 1.School of Economics and Business Administration,Tallinn University of Technology,Tallinn,Estonia |
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Abstract: | The least-squares method is used to obtain a stable algorithm for a system of linear inequalities as well as linear and nonlinear
programming. For these problems the solution with minimal norm for a system of linear inequalities is found by solving the
non-negative least-squares (NNLS) problem. Approximate and exact solutions of these problems are discussed. Attention is mainly
paid to finding the initial solution to an LP problem. For this purpose an NNLS problem is formulated, enabling finding the
initial solution to the primal or dual problem, which may turn out to be optimal. The presented methods are primarily suitable
for ill-conditioned and degenerate problems, as well as for LP problems for which the initial solution is not known. The algorithms
are illustrated using some test problems. |
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Keywords: | |
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