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  • Electronic Resource  (5)
  • Nonlinear complementarity problems  (2)
  • convex programming  (2)
  • unconstrained optimization reformulations  (2)
  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear Proximal Decomposition Method for Convex Programming (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 357-372 
    Details
    ISSN: 1573-2878
    Keywords: nonlinear proximal decomposition method ; Bregman functions ; convex programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we propose a new decomposition method for solving convex programming problems with separable structure. The proposed method is based on the decomposition method proposed by Chen and Teboulle and the nonlinear proximal point algorithm using the Bregman function. An advantage of the proposed method is that, by a suitable choice of the Bregman function, each subproblem becomes essentially the unconstrained minimization of a finite-valued convex function. Under appropriate assumptions, the method is globally convergent to a solution of the problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004655531273
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Unconstrained Optimization Reformulations of Variational Inequality Problems (1997)
    Springer
    Journal of optimization theory and applications 92 (1997), S. 439-456 
    Details
    ISSN: 1573-2878
    Keywords: Variational inequality problems ; unconstrained optimization reformulations ; global error bounds ; descent methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, Peng considered a merit function for the variational inequality problem (VIP), which constitutes an unconstrained differentiable optimization reformulation of VIP. In this paper, we generalize the merit function proposed by Peng and study various properties of the generalized function. We call this function the D-gap function. We give conditions under which any stationary point of the D-gap function is a solution of VIP and conditions under which it provides a global error bound for VIP. We also present a descent method for solving VIP based on the D-gap function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022660704427
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Penalty function theory for general convex programming problems (1978)
    Springer
    Journal of optimization theory and applications 24 (1978), S. 287-301 
    Details
    ISSN: 1573-2878
    Keywords: Penalty functions ; convex programming ; infimal convergence ; pointwise convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A class of penalty functions for solving convex programming problems with general constraint sets is considered. Convergence theorems for penalty methods are established by utilizing the concept of infimal convergence of a sequence of functions. It is shown that most existing penalty functions are included in our class of penalty functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933282
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    New NCP-Functions and Their Properties (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 115-135 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear complementarity problems ; NCP-functions ; merit functions ; unconstrained optimization reformulations ; error bounds ; bounded level sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently, Luo and Tseng proposed a class of merit functions for the nonlinear complementarity problem (NCP) and showed that it enjoys several interesting properties under some assumptions. In this paper, adopting a similar idea to that of Luo and Tseng, we present new merit functions for the NCP, which can be decomposed into component functions. We show that these merit functions not only share many properties with the one proposed by Luo and Tseng but also enjoy additional favorable properties owing to their decomposable structure. In particular, we present fairly mild conditions under which these merit functions have bounded level sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022659603268
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    On stationary points of the implicit Lagrangian for nonlinear complementarity problems (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 653-663 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear complementarity problems ; implicit Lagrangians ; equivalent differentiable optimization problems ; stationary points ; descent methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Mangasarian and Solodov have recently introduced an unconstrained optimization problem whose global minima are solutions of the nonlinear complementarity problem (NCP). In this paper, we show that, if the mapping involved in NCP has a positive-definite Jacobian, then any stationary point of the optimization problem actually solves NCP. We also discuss a descent method for solving the unconstrained optimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02191990
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    Paper (German National Licenses)
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