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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear programming via an exact penalty function: Asymptotic analysis (1982)
    Springer
    Mathematical programming 24 (1982), S. 123-136 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider the final stage of a ‘global’ method to solve the nonlinear programming problem. We prove 2-step superlinear convergence. In the process of analyzing this asymptotic behavior, we compare our method (theoretically) to the popular successive quadratic programming approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585100
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  • 2
    Electronic Resource
    Electronic Resource
    A projection method for the uncapacitated facility location problem (1990)
    Springer
    Mathematical programming 46 (1990), S. 273-298 
    Details
    ISSN: 1436-4646
    Keywords: Location ; projection methods ; computational study
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Several algorithms already exist for solving the uncapacitated facility location problem. The most efficient are based upon the solution of the strong linear programming relaxation. The dual of this relaxation has a condensed form which consists of minimizing a certain piecewise linear convex function. This paper presents a new method for solving the uncapacitated facility location problem based upon the exact solution of the condensed dual via orthogonal projections. The amount of work per iteration is of the same order as that of a simplex iteration for a linear program inm variables and constraints, wherem is the number of clients. For comparison, the underlying linear programming dual hasmn + m + n variables andmn +n constraints, wheren is the number of potential locations for the facilities. The method is flexible as it can handle side constraints. In particular, when there is a duality gap, the linear programming formulation can be strengthened by adding cuts. Numerical results for some classical test problems are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585746
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  • 3
    Electronic Resource
    Electronic Resource
    Nonlinear programming via an exact penalty function: Global analysis (1982)
    Springer
    Mathematical programming 24 (1982), S. 137-161 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we motivate and describe an algorithm to solve the nonlinear programming problem. The method is based on an exact penalty function and possesses both global and superlinear convergence properties. We establish the global qualities here (the superlinear nature is proven in [7]). The numerical implementation techniques are briefly discussed and preliminary numerical results are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585101
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  • 4
    Electronic Resource
    Electronic Resource
    On the Number of Inner Iterations Per Outer Iteration of a Globally Convergent Algorithm for Optimization with General Nonlinear Inequality Constraints and Simple Bounds (1997)
    Springer
    Computational optimization and applications 7 (1997), S. 41-69 
    Details
    ISSN: 1573-2894
    Keywords: Nonlinear optimization ; inequality constraints ; barrier methods ; complexity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper considers the number of inner iterations required per outeriteration for the algorithm proposed by Conn et al.[9]. We show that asymptotically, under suitable reasonable assumptions, a single inner iteration suffices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008667728545
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  • 5
    Electronic Resource
    Electronic Resource
    Second-order conditions for an exact penalty function (1980)
    Springer
    Mathematical programming 19 (1980), S. 178-185 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Exact Penalty Function ; Constrained Optimization ; Piecewise Differentiable
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we give first- and second-order conditions to characterize a local minimizer of an exact penalty function. The form of this characterization gives support to the claim that the exact penalty function and the nonlinear programming problem are closely related. In addition, we demonstrate that there exist arguments for the penalty function from which there are no descent directions even though these points are not minimizers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581639
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  • 6
    Electronic Resource
    Electronic Resource
    Erratum (1981)
    Springer
    Mathematical programming 21 (1981), S. 357-357 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584255
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  • 7
    Electronic Resource
    Electronic Resource
    Foreword (1990)
    Springer
    Mathematical programming 48 (1990), S. vii 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582248
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  • 8
    Electronic Resource
    Electronic Resource
    A network penalty method (1991)
    Springer
    Mathematical programming 50 (1991), S. 53-73 
    Details
    ISSN: 1436-4646
    Keywords: Network flows ; penalty functions ; network simplex
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the minimum cost network flow problem and describe how the non-linear penalty function methods of Conn and Bartels can be specialized to a combinatorial algorithm for this problem. We report on preliminary computational results which show that this method can require fewer pivots than the simplex method while the amount of work required for each pivot is comparable. The algorithm can be proven finite using a modification of Cunningham's strongly feasible basis pivoting rule.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01594924
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  • 9
    Electronic Resource
    Electronic Resource
    Convergence of quasi-Newton matrices generated by the symmetric rank one update (1991)
    Springer
    Mathematical programming 50 (1991), S. 177-195 
    Details
    ISSN: 1436-4646
    Keywords: Quasi-Newton updates ; convergence theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Quasi-Newton algorithms for unconstrained nonlinear minimization generate a sequence of matrices that can be considered as approximations of the objective function second derivatives. This paper gives conditions under which these approximations can be proved to converge globally to the true Hessian matrix, in the case where the Symmetric Rank One update formula is used. The rate of convergence is also examined and proven to be improving with the rate of convergence of the underlying iterates. The theory is confirmed by some numerical experiments that also show the convergence of the Hessian approximations to be substantially slower for other known quasi-Newton formulae.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01594934
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  • 10
    Electronic Resource
    Electronic Resource
    A note on exploiting structure when using slack variables (1994)
    Springer
    Mathematical programming 67 (1994), S. 89-97 
    Details
    ISSN: 1436-4646
    Keywords: 65K05 ; 90C30 ; Large-scale problems ; Nonlinear optimization ; Numerical algorithms ; Slack variables ; Augmented Lagrangian
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show how to exploit the structure inherent in the linear algebra for constrained nonlinear optimization problems when inequality constraints have been converted to equations by adding slack variables and the problem is solved using an augmented Lagrangian method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582214
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