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  • duality theorems  (1)
  • regular functions  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Duality and existence theory for nondifferentiable programming (1986)
    Springer
    Journal of optimization theory and applications 48 (1986), S. 451-458 
    Details
    ISSN: 1573-2878
    Keywords: Optimality conditions ; directional derivatives ; subdifferentials ; constraint qualifications ; stationary point problems ; duality theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Necessary and sufficient conditions of optimality are given for a nonlinear nondifferentiable program, where the constraints are defined via closed convex cones and their polars. These results are then used to obtain an existence theorem for the corresponding stationary point problem, under some convexity and regularity conditions on the functions involved, which also guarantee an optimal solution to the programming problem. Furthermore, a dual problem is defined, and a strong duality theorem is obtained under the assumption that the constraint sets of the primal and dual problems are nonempty.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940571
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A class of nonlinear complementarity problems for multifunctions (1987)
    Springer
    Journal of optimization theory and applications 53 (1987), S. 105-113 
    Details
    ISSN: 1573-2878
    Keywords: Complementarity problems ; subdifferentials ; multifunctions ; existence theorems ; regular functions ; monotone functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a continuous mapF:R n →R n and a lower semicontinuous positively homogeneous convex functionh:R n →R, the nonlinear complementarity problem considered here is to findxεR + n andy∈∂h(x), the subdifferential ofh atx, such thatF(x)+y≥0 andx T (F(x)+y)=0. Some existence theorems for the above problem are given under certain conditions on the mapF. An application to quasidifferentiable convex programming is also shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938819
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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