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  • Articles  (4,454)
  • Springer  (4,454)
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  • 2015-2019  (3,823)
  • 2005-2009
  • 1990-1994
  • 1980-1984  (631)
  • 2019  (3,823)
  • 1980  (631)
  • Computer Science  (4,454)
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  • Articles  (4,454)
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  • 2015-2019  (3,823)
  • 2005-2009
  • 1990-1994
  • 1980-1984  (631)
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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
    Weber's problem and weiszfeld's algorithm in general spaces (1980)
    Springer
    Mathematical programming 18 (1980), S. 186-196 
    Details
    ISSN: 1436-4646
    Keywords: Weber's Problem ; Weiszfeld's Method ; Optimal Location
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For solving the Euclidean distance Weber problem Weiszfeld proposed an iterative method. This method can also be applied to generalized Weber problems in Banach spaces. Examples for generalized Weber problems are: minimal surfaces with obstacles, Fermat's principle in geometrical optics and brachistochrones with obstacles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588313
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  • 4
    Electronic Resource
    Electronic Resource
    Borsuk's theorem through complementary pivoting (1980)
    Springer
    Mathematical programming 18 (1980), S. 84-88 
    Details
    ISSN: 1436-4646
    Keywords: Complementary Pivot Algorithms ; Triangulations ; Vector Labels ; Borsuk's Theorem on Antipodal Points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this short note a simple and constructive proof is given for Borsuk's theorem on antipodal points. This is done through a special application of the complementary pivoting algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588299
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  • 5
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1980)
    Springer
    Mathematical programming 18 (1980), S. 110-110 
    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/BF01588306
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  • 6
    Electronic Resource
    Electronic Resource
    A differential equation approach to nonlinear programming (1980)
    Springer
    Mathematical programming 18 (1980), S. 155-168 
    Details
    ISSN: 1436-4646
    Keywords: Constrained Optimization ; Differential Equation ; Global Solution ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A new method is presented for finding a local optimum of the equality constrained nonlinear programming problem. A nonlinear autonomous system is introduced as the base of the theory instead of usual approaches. The relation between critical points and local optima of the original optimization problem is proved. Asymptotic stability of the critical points is also proved. A numerical algorithm which is capable of finding local optima systematically at the quadratic rate of convergence is developed from a detailed analysis of the nature of trajectories and critical points. Some numerical results are given to show the efficiency of the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588311
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  • 7
    Electronic Resource
    Electronic Resource
    A generalization of the Frank—Wolfe theorem (1980)
    Springer
    Mathematical programming 18 (1980), S. 215-227 
    Details
    ISSN: 1436-4646
    Keywords: Frank—Wolfe Theorem ; Quadratic Programming ; Norm Coercive Functions ; Polyhedral Sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Frank—Wolfe theorem states that a quadratic function, bounded below on a nonempty polyhedral convex set, attains its infimum there. This paper gives sufficient conditions under which a function either attains its infimum on a nonempty polyhedral convex set or is unbounded below on some halfline of that set. Quadratic functions are shown to satisfy these sufficient conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588315
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  • 8
    Electronic Resource
    Electronic Resource
    Pseudo duality in mathematical programming: Unconstrained problems and problems with equality constraints (1980)
    Springer
    Mathematical programming 18 (1980), S. 248-273 
    Details
    ISSN: 1436-4646
    Keywords: Legendre Transform ; Stationary Points ; Convex Functions ; Duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this work non-convex programs are analyzed via Legendre transform. The first part includes definitions and the classification of programs that can be handled by the transformation. It is shown that differentiable functions that are represented as a sum of strictly concave and convex functions belong to this class. Conditions under which a function may have such representation are given. Pseudo duality is defined and the pseudo duality theorem for non linear programs with equality constraints is proved. The techniques described are constructive ones, and they enable tocalculate explicitly a pseudo dual once the primal program is given. Several examples are included. In the convex case these techniques enable the explicit calculation of the dual even in cases where direct calculation was not possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588322
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  • 9
    Electronic Resource
    Electronic Resource
    Steiner's problem and fagnano's result on the sphere (1980)
    Springer
    Mathematical programming 18 (1980), S. 286-290 
    Details
    ISSN: 1436-4646
    Keywords: Facility Location ; Steiner's Problem ; Location on the Sphere
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This note describes the nature of optimal solutions for the spherical Steiner-Weber location problem for the case of unit weights and either 3 or 4 demand points (requireing 4 demand points to lie in an open hemisphere). Geometrically appealing results which are necessary conditions for optimum solutions and spherical analogs of known planar results are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588324
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  • 10
    Electronic Resource
    Electronic Resource
    An economic interpretation of stochastic programs (1980)
    Springer
    Mathematical programming 18 (1980), S. 62-67 
    Details
    ISSN: 1436-4646
    Keywords: Economic Interpretation ; Mathematical Programming ; Duality ; Stochastic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this note is to interpret a class of stochastic programming problems in economic terms. The primal stochastic program is shown to represent a certain production program of an entrepreneur. The dual program, which is also a stochastic program, represents the problem of a contractor who desires to purchase the entrepreneur's resources and sell product back to him.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588297
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