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  • Articles  (2,863)
  • Springer  (2,863)
  • Springer Nature
  • 1980-1984  (2,863)
  • Computer Science  (2,863)
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  • Articles  (2,863)
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  • 1
    Electronic Resource
    Electronic Resource
    Shadow prices in nonconvex mathematical programming (1980)
    Springer
    Mathematical programming 19 (1980), S. 300-312 
    Details
    ISSN: 1436-4646
    Keywords: Equilibrium Prices ; Nonconvex Mathematical Programming ; Shadow Prices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper a definition is proposed for the concept of shadow prices in nonconvex programming. For a nonlinear program with equality and inequality constraints, existence of these prices and bounds for their possible values are obtained under the Mangasarian—Fromowitz regularity condition. Their exact values and some continuity properties are obtained under the more restrictive linear independence regularity condition. A definition of equilibrium prices is also proposed. Under convexity assumptions, all definitions and results coincide with those already known on this subject in convex programming.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581650
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  • 2
    Electronic Resource
    Electronic Resource
    Infinite retrogression in the Eaves—Saigal algorithm (1980)
    Springer
    Mathematical programming 19 (1980), S. 313-327 
    Details
    ISSN: 1436-4646
    Keywords: Retrogressing Paths ; Homotopy Method ; Fixed-point Algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For certain functionsf fromR n toR n , the Eaves—Saigal algorithm computes a path inR n × (0, 1] which converges to a zero off. In this case, it is shown that even whenf is of classC ∞ and has a unique zero, the converging path may retrogress infinitely many times.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581651
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  • 3
    Electronic Resource
    Electronic Resource
    On the number of solutions to a class of complementarity problems (1981)
    Springer
    Mathematical programming 21 (1981), S. 190-203 
    Details
    ISSN: 1436-4646
    Keywords: Complementarity Problem ; Cones ; Topological Degree
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider the problem of establishing the number of solutions to the complementarity problem. For the case when the Jacobian of the mapping has all principal minors negative, and satisfies a condition at infinity, we prove that the problem has either 0, 1, 2 or 3 solutions. We also show that when the Jacobian has all principal minors positive, and satisfies a condition at infinity, the problem has a unique solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584240
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  • 4
    Electronic Resource
    Electronic Resource
    Finding simplicial subdivisions of polytopes (1981)
    Springer
    Mathematical programming 21 (1981), S. 233-234 
    Details
    ISSN: 1436-4646
    Keywords: Polytope ; Subdivision ; Simplex ; Volume ; Centroid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Subdivisions of polytopes are described which place any chosen vertex in a (near-) minimal number of simplices. Ancillary procedures to find volumes and centroids of polytopes are indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584244
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  • 5
    Electronic Resource
    Electronic Resource
    Direct theorems in semi-infinite convex programming (1981)
    Springer
    Mathematical programming 21 (1981), S. 301-318 
    Details
    ISSN: 1436-4646
    Keywords: Semi-infinite Programs ; Open Helly-type Theorems ; Finite Subprograms ; Convex Programs ; Multi-criteria Programs ; Quasi-convex Programs ; Quasi-differentiable Programs
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a semi-infinite quasi-convex program with certain regularity conditions possesses finitely constrained subprograms with the same optimal value. This result is applied to various problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584251
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  • 6
    Electronic Resource
    Electronic Resource
    A statistical estimate of the structure of multi-extremal problems (1981)
    Springer
    Mathematical programming 21 (1981), S. 348-356 
    Details
    ISSN: 1436-4646
    Keywords: Multi-extremal Optimization ; Multinomial Distribution ; Bayes Estimate ; Monte Carlo
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The solution of ak-extremal problem is defined as the set of pairs (x i * , θi),i = 1, ⋯ ,k, where x t * isi th local minimum andθ i is the volume of the set of attraction of this minimum. A Bayesian estimate ofk and (θ 1 , ⋯ , θ k ) is constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584254
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  • 7
    Electronic Resource
    Electronic Resource
    On the use of penumbras in blocking and antiblocking theory (1982)
    Springer
    Mathematical programming 22 (1982), S. 71-81 
    Details
    ISSN: 1436-4646
    Keywords: Blocking ; Antiblocking ; Polarity ; Penumbra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract E. Johnson has recently shown that the concept of a penumbra leads to a simple geometric description of the blocker and antiblocker of a given set. Here we develop some basic results on penumbras which permit us to slightly generalize and simplify results on their relationship to blocking and antiblocking theory. In addition, motivated by the obvious symmetry of our results, we examine the effect of reversing the blocking and antiblocking operations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581026
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  • 8
    Electronic Resource
    Electronic Resource
    On the structure of all minimum cuts in a network and applications (1982)
    Springer
    Mathematical programming 22 (1982), S. 121-121 
    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/BF01581031
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  • 9
    Electronic Resource
    Electronic Resource
    Heuristics for the fixed cost median problem (1982)
    Springer
    Mathematical programming 22 (1982), S. 148-162 
    Details
    ISSN: 1436-4646
    Keywords: Set Covering Problem ; Median Problem ; Location Problems ; Heuristics ; Worst Case Analysis ; Continuous Location Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe in this paper polynomial heuristics for three important hard problems—the discrete fixed cost median problem (the plant location problem), the continuous fixed cost median problem in a Euclidean space, and the network fixed cost median problem with convex costs. The heuristics for all the three problems guarantee error ratios no worse than the logarithm of the number of customer points. The derivation of the heuristics is based on the presentation of all types of median problems discussed as a set covering problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581035
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  • 10
    Electronic Resource
    Electronic Resource
    On minimax optimization problems (1982)
    Springer
    Mathematical programming 22 (1982), S. 227-230 
    Details
    ISSN: 1436-4646
    Keywords: Minimax ; Nonconvex Optimization ; Stationary Points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give a short proof that in a convex minimax optimization problem ink dimensions there exist a subset ofk + 1 functions such that a solution to the minimax problem with thosek + 1 functions is a solution to the minimax problem with all functions. We show that convexity is necessary, and prove a similar theorem for stationary points when the functions are not necessarily convex but the gradient exists for each function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581038
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