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  • Articles  (37)
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  • Nonlinear programming  (37)
  • 2010-2014
  • 1985-1989  (24)
  • 1980-1984  (13)
  • Mathematics  (37)
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  • Books  (1)
  • Articles  (37)
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  • 1
    Electronic Resource
    Electronic Resource
    NLPQL: A fortran subroutine solving constrained nonlinear programming problems (1986)
    Springer
    Annals of operations research 5 (1986), S. 485-500 
    Details
    ISSN: 1572-9338
    Keywords: Nonlinear programming ; sequential quadratic programming method ; numerical implementation ; test results
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract NLPQL is a FORTRAN implementation of a sequential quadratic programming method for solving nonlinearly constrained optimization problems with differentiable objective and constraint functions. At each iteration, the search direction is the solution of a quadratic programming subproblem. This paper discusses the organization of NLPQL, including the formulation of the subproblem and the information that must be provided by a user. A summary is given of the performance of different algorithmic options of NLPQL on a collection of test problems (115 hand-selected or application problems, 320 randomly generated problems). The performance of NLPQL is compared with that of some other available codes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02022087
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  • 2
    Electronic Resource
    Electronic Resource
    Integrating modeling, algorithm design, and computational implementation to solve a large-scale non-linear mixed integer programming problem (1986)
    Springer
    Annals of operations research 5 (1986), S. 395-411 
    Details
    ISSN: 1572-9338
    Keywords: Nonlinear programming ; decomposition ; branch and bound ; network ; transportation ; mixed integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02022082
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  • 3
    Electronic Resource
    Electronic Resource
    A successive quadratic programming algorithm with global and superlinear convergence properties (1986)
    Springer
    Mathematical programming 35 (1986), S. 253-264 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear programming ; successive quadratic programming ; Maratos effect ; exact penalty function ; superlinear convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580879
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlinear programming and nonsmooth optimization by successive linear programming (1989)
    Springer
    Mathematical programming 43 (1989), S. 235-256 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear programming ; nonsmooth optimization ; global convergence ; superlinear convergence ; trust region method ; Coleman-Conn method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Methods are considered for solving nonlinear programming problems using an exactl 1 penalty function. LP-like subproblems incorporating a trust region constraint are solved successively both to estimate the active set and to provide a foundation for proving global convergence. In one particular method, second order information is represented by approximating the reduced Hessian matrix, and Coleman-Conn steps are taken. A criterion for accepting these steps is given which enables the superlinear convergence properties of the Coleman-Conn method to be retained whilst preserving global convergence and avoiding the Maratos effect. The methods generalize to solve a wide range of composite nonsmooth optimization problems and the theory is presented in this general setting. A range of numerical experiments on small test problems is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582292
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  • 5
    Electronic Resource
    Electronic Resource
    Computable bounds on parametric solutions of convex problems (1988)
    Springer
    Mathematical programming 40 (1988), S. 213-221 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear programming ; convex programming ; sensitivity and stability analysis ; parametric solutions ; optimal solution bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a new method for computing bounds on parametric solutions of convex problems. The approach is based on a uniform quadratic underestimation of the objective function and a simple technique for the calculation of bounds on the optimal value function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580732
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  • 6
    Electronic Resource
    Electronic Resource
    Homotopy techniques in linear programming (1986)
    Springer
    Algorithmica 1 (1986), S. 529-535 
    Details
    ISSN: 1432-0541
    Keywords: Homotopy ; Linear programming ; Interior point methods ; Nonlinear programming ; Karmarkar's method ; Quadratic regularization ; Path-following
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this note, we consider the solution of a linear program, using suitably adapted homotopy techniques of nonlinear programming and equation solving that move through the interior of the polytope of feasible solutions. The homotopy is defined by means of a quadratic regularizing term in an appropriate metric. We also briefly discuss algorithmic implications and connections with the affine variant of Karmarkar's method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840461
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  • 7
    Electronic Resource
    Electronic Resource
    Convergence of a Tuy-type algorithm for concave minimization subject to linear inequality constraints (1981)
    Springer
    Applied mathematics & optimization 7 (1981), S. 1-9 
    Details
    ISSN: 1432-0606
    Keywords: Nonlinear programming ; nonconvex programming ; concave minimization ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A modification of Tuy's cone splitting algorithm for minimizing a concave function subject to linear inequality constraints is shown to be convergent by demonstrating that the limit of a sequence of constructed convex polytopes contains the feasible region. No geometric tolerance parameters are required.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442106
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  • 8
    Electronic Resource
    Electronic Resource
    Numerical study of some feasible direction methods in mathematical programming (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 1-23 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; feasible directions ; linear least squares ; Householder orthogonal factorization ; Gauss-Jordan factorization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Some feasible direction methods for the minimization of a linearly constrained convex function are studied. Special emphasis is placed on the analysis of the procedures which find the search direction, by developing active set methods which use orthogonal or Gauss-Jordan-like transformations. Numerical experiments are performed on a class of quadratic problems depending on two parameters, related to the conditioning of the matrix associated with the quadratic form and the matrix of active constraints at the optimal point. Results are given for the rate of convergence and the average iteration time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934629
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  • 9
    Electronic Resource
    Electronic Resource
    Theoretical properties and numerical tests of an efficient nonlinear decomposition algorithm (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 211-227 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; decomposition algorithm ; convexity ; convergence ; SUMT algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Kronsjö's nonlinear generalization (Ref. 1) of Benders' algorithm (Ref. 2) is reviewed. At each iteration, this algorithm produces upper and lower bounds to the true optimum, and the sequence of lower bounds is increasing. The algorithm is modified, so that the sequence of upper bounds is ε-decreasing as well. The two versions are tested numerically using an ALGOL program originally written by Wong (Ref. 3), incorporating the SUMT method (Fiacco and McCormick, Refs. 4 and 5). The two versions are compared against each other, and the problem of the optimal degree of decomposition is considered. Finally, an attempt is made to express the computer time required to solve the test problems as a function of master problem size, number of subproblems, and average subproblem size.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934496
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  • 10
    Electronic Resource
    Electronic Resource
    Second-order and related extremality conditions in nonlinear programming (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 143-165 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; local extrema second-order conditions ; constraint qualification ; extremality conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the problem of characterizing a local minimum of a mathematical programming problem with equality and inequality constraints. The main object is to derive second-order conditions, involving the Hessians of the functions, or related results where some other curvature information is used. The necessary conditions are of the Fritz John type and do not require a constraint qualification. Both the necessary conditions and the sufficient conditions are given in equivalent pairs of primal and dual formulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934107
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