The objective function used when determining parameters in models for multiphase flow in porous media can have multiple local minima. The challenge is then to find the global minimum and also to determine the uniqueness of the optimized parameter values. A method for mapping out local minima to search for the global minimum by traversing regions of first order saddle points on the objective fun...

A fast community detection algorithm based on a q-state Potts model is presented. Communities (groups of densely interconnected nodes that are only loosely connected to the rest of the network) are found to coincide with the domains of equal spin value in the minima of a modified Potts spin glass Hamiltonian. Comparing global and local minima of the Hamiltonian allows for the detection of overl...

A Monte Carlo-minimization method has been developed to overcome the multiple-minima problem. The Metropolis Monte Carlo sampling, assisted by energy minimization, surmounts intervening barriers in moving through successive discrete local minima in the multidimensional energy surface. The method has located the lowest-energy minimum thus far reported for the brain pentapeptide [Met5]enkephalin ...

An improved strategy for finding the ab initio global minimum of SixHy clusters based on a cluster genetic algorithm (CGA) is presented. Four new mutation operators are introduced which better facilitate retention of desirable structural features between the different generations of clusters in the CGA. The new CGA generally finds global minima with fewer energy evaluations and is now able to f...

We report a blind test of lattice-model-based search strategies for finding global minima of model protein chains. One of us (E.I.S.) selected 10 compact conformations of 48-mer chains on the three-dimensional cubic lattice and used their inverse folding algorithm to design HP (H, hydrophobic; P, polar) sequences that should fold to those "target" structures. The sequences, but not the structur...

We study on-line backpropagation and show that the existing theoretical descriptions are strictly valid only on relatively short time scales or in the vicinity of (local) minima of the backpropagation error potential. Qualitative global features (e.g., why is it much easier to escape from local minima than from global minima) may also be explained by these local descriptions, but the current ap...

We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global minimum. This condition can be explicitly evaluated at the discrete level. Furthermore, we prove that if the above condition holds uniformly with respect to t...