1,720,968 research outputs found
Convergence properties of a class of reduced gradient algorithms in linearly constrained minimization
No full text
Properties and numerical testing of a parallel global optimization algorithm
No full textIn the framework of multistart and local search algorithms that find
the global minimum of a real function f(x), x ∈ S ⊆ Rn, Gaviano et alias proposed a rule for deciding, as soon as a local minimum has been found, whether to perform or not a new local minimization. That rule was designed
to minimize the average local computational cost eval1(·) required to move from the current local minimum to a new one. In this paper the expression of the cost eval2(·) of the entire process of getting a global minimum is found and investigated; it is shown that eval2(·) has among its components eval1(·)
and can be only monotonically increasing or decreasing; that is, it exhibits the
same property of eval1(·). Moreover, a counterexample is given that shows
that the optimal values given by eval1(·) and eval2(·) might not agree. Further,
computational experiments of a parallel algorithm that uses the above rule are
carried out in a MatLab environment
Complexity of general continuous minimization problems: A survey
No full textThe problem of finding a local or a global minimum of a real function on a set S, a subset of Rn, provides a
mathematical tool for solving many real world problems.
Deterministic and stochastic algorithms have been proposed in the case of f being a general nonlinear function. The numerical cost of these algorithms, that can be the number of function evaluations or the number of elementary operations required when executed, has been investigated in the last few years. In this paper we survey the main results by classifying them according to the field they refer to: local minimization, global minimization and checking the optimality conditions.
Further, few results concerning the information that an algorithm may use, are surveyed
A global minimization algorithm for Lipschitz functions
No full textThe global optimization problem min f(x), x in S with S=[a,b], a, b in Rn and f(x) satisfying the Lipschitz condition |f(x)-f(y)|≤l|x-y| (the maximum norm) for all x,y in S, l>0,
is considered. To solve it, a region-search algorithm is
introduced. This combines a local minimum algorithm with a procedure that decreases the measure of the region where the global minimum is located. Specifically, by making use of the
Lipschitz condition, at each algorithm iteration a sequence of intervals {s_j} s_j a subset S is constructed, with the
property that a global minimum is in s_j. A convergence property of the algorithm is given. Further, numerical experiments
are carried out; these show that the algorithm is effective
for problems of small dimension
Bayesian stopping rules for improvement of local minima algorithms in global optimization
No full text- …
