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  • parametric programming  (2)
  • Springer  (2)
  • American Association for the Advancement of Science (AAAS)
  • 1
    Electronic Resource
    Electronic Resource
    Algorithms for parametric nonconvex programming (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 319-340 
    Details
    ISSN: 1573-2878
    Keywords: Nonconvex programming ; parametric programming ; branch-and-bound methods ; global minimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a general family of nonconvex programming problems. All of the objective functions of the problems in this family are identical, but their feasibility regions depend upon a parameter ϑ. This family of problems is called a parametric nonconvex program (PNP). Solving (PNP) means finding an optimal solution for every program in the family. A prototype branch-and-bound algorithm is presented for solving (PNP). By modifying a prototype algorithm for solving a single nonconvex program, this algorithm solves (PNP) in one branch-and-bound search. To implement the algorithm, certain compact partitions and underestimating functions must be formed in an appropriate manner. We present an algorithm for solving a particular (PNP) which implements the prototype algorithm by forming compact partitions and underestimating functions based upon rules given by Falk and Soland. The programs in this (PNP) have the same concave objective function, but their feasibility regions are described by linear constraints with differing right-hand sides. Computational experience with this algorithm is reported for various problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935342
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  • 2
    Electronic Resource
    Electronic Resource
    On the optimal value function for certain linear programs with unbounded optimal solution sets (1985)
    Springer
    Journal of optimization theory and applications 46 (1985), S. 55-66 
    Details
    ISSN: 1573-2878
    Keywords: Optimal value function ; linear programming ; sensitivity analysis ; parametric programming ; multiple-objective linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Often, the coefficients of a linear programming problem represent estimates of true values of data or are subject to systematic variations. In such cases, it is useful to perturb the original data and to either compute, estimate, or otherwise describe the values of the functionf which gives the optimal value of the linear program for each perturbation. If the right-hand derivative off at a chosen point exists and is calculated, then the values off in a neighborhood of that point can be estimated. However, if the optimal solution set of either the primal problem or the dual problem is unbounded, then this derivative may not exist. In this note, we show that, frequently, even if the primal problem or the dual problem has an unbounded optimal solution set, the nature of the values off at points near a given point can be investigated. To illustrate the potential utility of our results, their application to two types of problems is also explained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938759
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    Paper (German National Licenses)
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