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  • 1
    Electronic Resource
    Electronic Resource
    Convexification of a noninferior frontier (1996)
    Springer
    Journal of optimization theory and applications 88 (1996), S. 177-196 
    Details
    ISSN: 1573-2878
    Keywords: Multiobjective optimization ; nonconvex optimization ; convexification ; noninferior frontier
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The convexity of a noninferior frontier can be achieved in an appropriate equivalent objective space for general nonconvex multi-objective optimization problems. Specifically, this paper proves that applying thep-power to the objective functions can act as a convexification scheme for a noninferior frontier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02192028
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  • 2
    Electronic Resource
    Electronic Resource
    Exponential Transformation in Convexifying a Noninferior Frontier and Exponential Generating Method (1998)
    Springer
    Journal of optimization theory and applications 99 (1998), S. 183-199 
    Details
    ISSN: 1573-2878
    Keywords: Multiobjective optimization ; nonconvex optimization ; convexification ; noninferior frontier ; exponential generating method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The convexification of a noninferior frontier can be achieved in an appropriate equivalent objective space for general nonconvex multiobjective optimization problems. Specifically, this paper proves that taking the exponentials of the objective functions can act as a convexification scheme. This convexification scheme further leads to the exponential generating method that guarantees the identification of the entire set of noninferior solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021708412776
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  • 3
    Electronic Resource
    Electronic Resource
    Value-Estimation Function Method for Constrained Global Optimization (1999)
    Springer
    Journal of optimization theory and applications 102 (1999), S. 385-409 
    Details
    ISSN: 1573-2878
    Keywords: Constrained global optimization ; nonconvex optimization ; smoothing technique ; generalized Newton method ; bisection method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A novel value-estimation function method for global optimization problems with inequality constraints is proposed in this paper. The value-estimation function formulation is an auxiliary unconstrained optimization problem with a univariate parameter that represents an estimated optimal value of the objective function of the original optimization problem. A solution is optimal to the original problem if and only if it is also optimal to the auxiliary unconstrained optimization with the parameter set at the optimal objective value of the original problem, which turns out to be the unique root of a basic value-estimation function. A logarithmic-exponential value-estimation function formulation is further developed to acquire computational tractability and efficiency. The optimal objective value of the original problem as well as the optimal solution are sought iteratively by applying either a generalized Newton method or a bisection method to the logarithmic-exponential value-estimation function formulation. The convergence properties of the solution algorithms guarantee the identification of an approximate optimal solution of the original problem, up to any predetermined degree of accuracy, within a finite number of iterations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021736608968
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