A new algorithm is presented for the location of the global minimum of a multiple minima problem. It begins with a series of randomly placed probes in phase space, and then uses an iterative Gaussian redistribution of the worst probes into better regions of phase space until all probes converge to a single point. The method quickly converges, does not require derivatives, and is resistant to be...

Optimization techniques have been extensively used in a variety of physical problems in Many-Body systems such as the construction of optical potentials, phase shift analyses, variational calculations, neural network training, etc. In the field of Few-Body systems however, their use is rather limited although there are cases where the method could be very useful. A subtle feature is that when t...

Given a function on Rn with many multiple local minima we approximate it from below, via concave minimization, with a piecewise-linear convex function by using sample points from the given function. The piecewise-linear function is then minimized using a single linear program to obtain an approximation to the global minimum of the original function. Successive shrinking of the original search r...

Motivated by the fact that important real-life problems, such as the protein docking problem, can be accurately modeled by minimizing a nonconvex piecewise-quadratic function, a nonconvex underestimator is constructed as the minimum of a finite number of strictly convex quadratic functions. The nonconvex underestimator is generated by minimizing a linear function on a reverse convex region and ...

The Stability Index Method (SIM) combines stochastic and deterministic algorithms to find global minima of multidimensional functions. The functions may be nonsmooth and may have multiple local minima. The method examines the change of the diameters of the minimizing sets for its stopping criterion. At first, the algorithm uses the uniform random distribution in the admissible set. Then normal ...

We consider the least-squares (L2) triangulation problem and structure-and-motion with known rotatation, or known plane. Although optimal algorithms have been given for these algorithms under an L-infinity cost function, finding optimal least-squares (L2) solutions to these problems is difficult, since the cost functions are not convex, and in the worst case can have multiple minima. Iterative ...

We show how certain nonconvex optimization problems that arise in image processing and computer vision can be restated as convex minimization problems. This allows, in particular, the finding of global minimizers via standard convex minimization schemes.

where δif only needs to be accounted for if the applied loads influence the virtual crack rotation, e.g. due to crack face tractions and body-type loads. Also, it is worth observing that, non-zero contributions to the variations δiK, δif occur only in those elements that experience the virtual crack rotation. The rates of the energy release rate, Hsij are obtained by differentiating Gsi in (5) ...

This paper investigates error-entropy-minimization in adaptive systems training. We prove the equivalence between minimization of error’s Renyi entropy of order and minimization of a Csiszar distance measure between the densities of desired and system outputs. A nonparametric estimator for Renyi’s entropy is presented, and it is shown that the global minimum of this estimator is the same as the...

The optimal attitude estimate is often defined as the solution to a minimization problem. When the objective function of the minimization problem is quadratic in the attitude matrix or equivalently quartic in the attitude quaternion, for example, in GPS attitude determination, gradient-based iterative algorithms are usually used, which can only find the local minimizer. A novel numerical method...