A new unbiased global optimization approach is proposed, based on quantum staging path integral Monte Carlo sampling and local minimization of individual imaginary time slices. This algorithm uses the quantum tunneling effect to speed up the crossing of energy barriers. This method differs in important ways from previous work on quantum annealing and is able to find all the global minima of Len...

N -dimensional vectors ) ,..., , ( 2 1 N s s s = s will be called configuration vectors. They define N 2 possible states of the system (the configurations), among which the optimal configuration with regard to the objective function ) (s E has to be found. The number of different states increases exponentially, when N increases. Already if N > 50, it is almost impossible to solve the problem by...

In this paper we show an abstract theorem that can be used to prove the existence of solution for a class elliptic equation considered in Berestycki–Lions (Arch Ration Mech Anal 82:313–345, 1983) and related problems. Moreover, use zero mass problems has multiple solutions, which is novelty type problem.

We study the global and local convergence of a generic half-quadratic optimization algorithm inspired from the dual energy formulation of Geman and Reynolds [IEEE Trans. Pattern Anal. Mach. Intell., 14 (1992), pp. 367–383]. The target application is the minimization of C convex and nonconvex objective functionals arising in regularized image reconstruction. Our global convergence proofs are bas...

We propose a new PAC-Bayesian bound and a way of constructing a hypothesis space, so that the bound is convex in the posterior distribution and also convex in a trade-off parameter between empirical performance of the posterior distribution and its complexity. The complexity is measured by the Kullback-Leibler divergence to a prior. We derive an alternating procedure for minimizing the bound. W...

Energy minimization e orts to predict polypeptide structures assume their native conformation corre sponds to the global minimum free energy state Given this assumption the problem becomes that of develop ing e cient global optimization techniques applicable to polypeptide energy models This general structure prediction objective is also known as the protein fold ing problem Our prediction algo...

There is a growing need in computer vision applications for stereopsis, requiring not only accurate distance but also fast and compact physical implementation. Global energy minimization techniques provide remarkably precise results. But they suffer from huge computational complexity. One of the main challenges is to parallelize the iterative computation, solving the memory access problem betwe...

When the electron density in a crystal or a quasicrystal is reconstructed from its Fourier modes, the global minimum value of the density is sensitively dependent on the relative phases of the modes. The set of phases that maximizes the value of the global minimum corresponds, by positivity of the density, to the density having the minimum total charge that is consistent with the measured Fouri...