tive deenite and X is a local minimizer of. To the best of our knowledge, this is the rst formal demonstration of a nonglobal minimizer of the stress criterion. 4 Discussion We now know that nonglobal minimizers of the stress criterion can exist. However, because of the tendency of SMACOF-I to terminate prematurely, the prevalence of nonglobal minimizers may have been overestimated in previous ...

We introduce a new T-F function for solving discrete general minimization problems with a general function over box-constrained domain. A T-F function is constructed at a local minimizer of the objective function such that it achieves local maximum at the current solution. Moreover, a local minimizer of the T-F function leads to a new solution to the original problem with lower objective functi...

We investigate a fast optimization method for determining the minimizer of the negative Poisson likelihood function for the global analysis of fluorescence lifetime microscopy. Using the alternating optimization strategy, we iteratively solve a non-convex optimization problem to estimate the lifetime parameters and a convex optimization problem to estimate the concentration parameters. We effec...

We show that if (u,K) is a global minimizer for the Mumford-Shah functional in R , and if K is a smooth enough cone, then (modulo constants) u is a homogenous function of degree 1 2 . We deduce some applications in R as for instance that an angular sector cannot be the singular set of a global minimizer, that if K is a half-plane then u is the corresponding cracktip function of two variables, o...

We investigate unconstrained optimization with an objective function that has an unknown and possibly large number of local minima. By varying the selection and termination criteria, we obtain several variants of the Moore-Skelboe algorithm for distinct tasks in nonconvex global optimization. All of these terminate after having found the best answer that is possible, given the precision of 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...

We consider the problem of minimizing a nonlinear discrete function with L-/M-convexity proposed in the theory of discrete convex analysis. For this problem, steepest descent algorithms and steepest descent scaling algorithms are known. In this paper, we use continuous relaxation approach which minimizes the continuous variable version first in order to find a good initial solution of a steepes...

In this paper we propose a form of the DIRECT algorithm that is strongly biased toward local search. This form should do well for small problems with a single global minimizer and only a few local minimizers. We motivate our formulation with some results on how the original formulation of the DIRECT algorithm clusters its search near a global minimizer. We report on the performance of our algor...

Remark. The notation in condition (iii) reflects the possibility that ḣ might fail to exist at finitely many points. (Various alternative ways to deal with this possibility exist; none is completely satisfactory.) There is an obvious heierarchy in these concepts: every global minimizer also satisfies the criteria to lie in each of the local categories listed above. Any strong local minimizer is...