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  • Articles  (5)
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  • Mathematical programming  (5)
  • 1985-1989
  • 1980-1984  (5)
  • 1960-1964
  • 1940-1944
  • 1981  (5)
  • Mathematics  (5)
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  • Articles  (5)
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  • 1985-1989
  • 1980-1984  (5)
  • 1960-1964
  • 1940-1944
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  • Mathematics  (5)
  • 1
    Electronic Resource
    Electronic Resource
    A minimization method for the sum of a convex function and a continuously differentiable function (1981)
    Springer
    Journal of optimization theory and applications 33 (1981), S. 9-23 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; nonconvex nondifferentiable optimization problems ; subgradients ; critical points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a method for finding the minimum for a class of nonconvex and nondifferentiable functions consisting of the sum of a convex function and a continuously differentiable function. The algorithm is a descent method which generates successive search directions by solving successive convex subproblems. The algorithm is shown to converge to a critical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935173
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the use of purely finitely additive multipliers in mathematical programming (1981)
    Springer
    Journal of optimization theory and applications 33 (1981), S. 37-55 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; duality ; countably additive multipliers ; purely finitely additive multipliers ; singular nonpositivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, duality results are obtained for the problem of finding α=inf{f(x):g(x)⩽0,g(x)∈Y,x∈C}, where the constrainst spaceY is someL ∞-space, by using the norm topology ofY. The corresponding multiplier is the sum of a countably additive part and a purely finitely additive part. Conditions are given such that the purely finitely additive part may be discarded.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935175
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  • 3
    Electronic Resource
    Electronic Resource
    Optimality conditions using sum-convex approximations (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 475-495 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; convex approximations ; theorems of the alternative ; optimality conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is to give necessary and sufficient conditions of optimality for a general mathematical programming problem, using not a linear approximation to the constraint function but an approximation possessing certain convexity properties. Such approximations are called sum-convex. Theorems of the alternative involving sum-convex functions are also presented as part of the proof.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934928
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  • 4
    Electronic Resource
    Electronic Resource
    Pseudo-duality and saddle points (1981)
    Springer
    Journal of optimization theory and applications 33 (1981), S. 325-347 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; stationary points ; barrier functions ; augmented Lagrangians
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Results associated with saddle-type stationary points are described. It is shown that barrier-type functions are pseudo-duals of generalized Lagrangian functions, while augmented Lagrangians are pseudo-duals of the regular Lagrangian function. An application of pseudo-duality to a min-max problem is illustrated, together with several other examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935248
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  • 5
    Electronic Resource
    Electronic Resource
    Stability theorems for 2×2 hypermatrices (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 1-7 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; control theory ; numerical methods ; convergence theorems ; stability theorems ; discrete-time dynamical systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, stability properties of 2×2 hypermatrices of the form $$\left[ {\begin{array}{*{20}c} { \in {\rm A} \in {\rm B}} \\ {CD} \\ \end{array} } \right]$$ are investigated, where ε is a small parameter. Stability theorems on these and similar matrices play an important role in the convergence analysis of certain numerical methods of mathematical programming and control theory, as pointed out in Refs. 1–3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934699
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