The problem of optimizing some contiuous function over the efficient set of a multiple objective programming problem can be formulated as a nonconvex global optimization problem with special structure. Based on the co...
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The problem of optimizing some contiuous function over the efficient set of a multiple objective programming problem can be formulated as a nonconvex global optimization problem with special structure. Based on the conical branch and bound algorithm in global optimization, we establish an algorithm for optimizing over efficient sets and discuss about the implementation of this algorithm for some interesting special cases including the case of biobjective programming problems.
A new conical algorithm is developed for finding the global minimum of a concave function over a polytope. To ensure faster convergence and overcome some major drawbacks of previous conical algorithms, a normal (rathe...
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A new conical algorithm is developed for finding the global minimum of a concave function over a polytope. To ensure faster convergence and overcome some major drawbacks of previous conical algorithms, a normal (rather than exhaustive) subdivision process is used.
The conical algorithm is a global optimization algorithm proposed by Tuy in 1964 to solve concave minimization problems. Introducing the concept of pseudo-nonsingularity, we give an alternative proof of convergence of...
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The conical algorithm is a global optimization algorithm proposed by Tuy in 1964 to solve concave minimization problems. Introducing the concept of pseudo-nonsingularity, we give an alternative proof of convergence of the algorithm with the -subdivision rule. We also develop a new convergent subdivision rule, named -bisection, and report numerical results of comparing it with the usual omega-subdivision.
A class of exhaustive cone splitting procedures is developed and is shown to perform substantially better than the bisection procedure in conical algorithms for concave minimization. Computational experiments are repo...
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