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The general principle of the structural risk minimization can be implemented in many different ways.
Its minimization can be carried out numerically, using, for example, the method of steepest descent".
The minimization can be solved with local, semi-global and global algorithms.
Sparse reconstruction methods based on l 1-norm minimization can be achieved by second-order cone programming (SOCP).
The minimization can be accomplished analytically, and the resulting nonlinear system of equations solved using a Newton Raphson procedure that integrates naturally with standard nonlinear finite element computations.
It has been shown that the superstructure aimed at the wastes minimization can be systematically formulated on the basis of the proposed strategy.
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Although it is NP-hard to find the global optimal solution of (l_{p} -minimization, a l_{p} -minimization be done in polynomialocale [24].
In the mixture prior, given dω and a set of prototypes, we define the posterior loss as And similarly define as the parameters that minimize this loss: This minimization problem can be solved by running P (the number of prototypes) minimization problems, one per prototype.
Any minimization method can be applied to minimize J.
In this paper, we aim at providing an approximation theory for the rank minimization problem, and prove that a rank minimization problem can be approximated to any level of accuracy via continuous optimization (especially, linear and nonlinear semidefinite programming) problems.
Now, the outage probability minimization problem can be turned to the problem of minimizing and simultaneously with respect to, that is,, which is a multicriterion optimization problem [27].
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