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  • 1
    Electronic Resource
    Electronic Resource
    Isotone solutions of parametric linear complementarity problems (1977)
    Springer
    Mathematical programming 12 (1977), S. 48-59 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The parametric linear complementarity problem is given by the conditions:q + αp + Mz ⩾ 0,α ⩾ 0,z ⩾ 0,z T (q + αp + Mz) = 0. Under the assumption thatM is a P-matrix, Cottle proved that the solution mapz(α) of the above problem is montonically nondecreasing in the parameterα for every nonnegativeq and everyp if and only ifM is a Minkowski matrix. This paper examines whether a similar result holds in various other settings including a nonlinear case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01593768
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the connectedness of the set of almost complementary paths of a linear complementarity problem (1979)
    Springer
    Mathematical programming 16 (1979), S. 384-385 
    Details
    ISSN: 1436-4646
    Keywords: Linear Complementarity Problem ; Bimatrix Game ; Connectedness ; Almost Complementary Paths
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582124
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The number of solutions of a class of linear complementarity problems (1979)
    Springer
    Mathematical programming 17 (1979), S. 104-105 
    Details
    ISSN: 1436-4646
    Keywords: Complementarity Problem ; Number of Solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588229
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A parametric linear complementarity problem involving derivatives (1978)
    Springer
    Mathematical programming 15 (1978), S. 146-154 
    Details
    ISSN: 1436-4646
    Keywords: Linear Complementarity Problem ; Principal Pivoting Algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The problem considered in this paper is given by the conditions:w = q + tp + Mz, w ≥ 0,ż ≥ 0,w T ż = 0, where a dot denotes the derivative with respect to the scalar parametert ≥ 0. In this problem,q, p aren-vectors withq ≥ 0 andM is an byn P-matrix. This problem arises in a certain basic problem in the field of structural mechanics. The main result in this paper is the existence and uniqueness theorem of a solution to this problem. The existence proof is constructive providing a computational method of obtaining the solution asymptotically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609013
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    A mathematical programming method for the inelastic analysis of reinforced concrete frames (1977)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 11 (1977), S. 1137-1154 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mathematical programming method is presented for solving problems of (i) determining the moments and rotations and (ii) determining the safety factor of reinforced concrete frames. The proposed method is essentially a reformulation of those developed by De Donato and Maier. However, the reformulation results in a new mathematical programming model for which an efficient algorithm is developed. The advantage of the proposed method is mainly computational; in fact it requires roughly one half computer time and storage space as compared with those De Donato and Maier employ to solve the same problem.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620110709
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  • 6
    Electronic Resource
    Electronic Resource
    Piecewise linear elastic-plastic analysis (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 757-767 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The purpose of this paper is to show that a mathematical programming method, due to Maier and his co-workers, of nonlinear structural analysis can be rerformulated so that greater computational efficiences are achived. The methods are designed for a class of elastic-plastic structures under ‘piecewise linear’ assumptions and solve among others the problem of determining the stresses and strains in the structure. The reformulation gives rise to a class of mathematical programming problems calles a ‘n by dn linear complementarity problem’, for which the author has developed an efficient algorithm. It will be explained why and by how much the proposed method (the reformulation and its solution by the author's algorithm) solves the structural problems more efficiently than the existing one. Results of a systematic computer experiment supporting the efficiency of the proposed method are also presented.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620140509
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    A decomposition procedure for large-scale optimum plastic design problemsSponsored by the United States Army under Contract Nos. DAAG29-75-C-0024 and DAAG29-80-C-0041. (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 873-889 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A decomposition procedure is proposed in this paper for solving a class of large-scale optimum design problems for perfectly-plastic structures under several alternative loading conditions. The conventional finite element method is used to cast the problem into a finite dimensional constrained nonlinear programming problem. Structures of practically meaningful size and complexity tend to give rise to a large number of variables and constraints in the corresponding mathematical model. The difficulty is that the state-of-the-art mathematical programming theory does not provide reliable and efficient ways of solving large-scale constrained nonlinear programming problems. The natural idea to deal with the large-scale structural problem is somehow to decompose the problem into a collection of small-size problems each of which represents an analysis of the behaviour of each finite element under a single loading condition. This paper proposes one such way of decomposition based on duality theory and a recently developed iterative algorithm called the proximal point algorithm.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620190609
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    Paper (German National Licenses)
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