We consider the problem of global convergence of Godard equalizers in the special case of binary (2-PAM) input signals , when the channel impulse response is complex. We present a class of global minima of all Godard equalizers for this case, which do not correspond to settings free of inter-symbol-interference (ISI). The equalizer output corresponding to these global minima appears as a four-p...

Kwanghsi Wang and V. McKoy Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125 (Received 1 December 1995) Using N2 2s21 u photoionization as an example, we present the first measurements and calculations of photoion vibrational distributions for an extended energy range (5 # Ek # 230 eV). The results show a striking breakdown of the F...

We provide the global optimization community with new optimality proofs for 6 deceptive benchmark functions (5 bound-constrained functions and one nonlinearly constrained problem). These highly multimodal nonlinear test problems are among the most challenging benchmark functions for global optimization solvers; some have not been solved even with approximate methods. The global optima that we r...

* Correspondence: [email protected] Department of Mathematics, School of Science, Shandong University of Technology, Zibo, 255049, China Full list of author information is available at the end of the article Abstract In this paper, we study the concept of weak sharp minima using two different approaches. One is transforming weak sharp minima to an optimization problem; another is using conju...

We consider the problem of minimizing the Lagrangian ∫ [F (∇u)+f u] among functions on Ω ⊂ R with given boundary datum φ. We prove Lipschitz regularity up to the boundary for solutions of this problem, provided Ω is convex and φ satisfies the bounded slope condition. The convex function F is required to satisfy a qualified form of uniform convexity only outside a ball and no growth assumptions ...

We prove that there exists a gain function ((t); (t)) t0 such that the solution of the SDE dx t = (t)(? grad U(x t)dt + (t)dB t) 'settles' down on the set of global minima of U. In particular the existence of a gain function ((t)) t0 so that y t satisfying dy t = (t)(? grad U(y t)dt + dB t) converges to the set of the global minima of U is veriied. Then we apply the results to the Robbins-Monro...

Learning new representations in machine learning is often tackled using a factorization of the data. For many such problems, including sparse coding and matrix completion, learning these factorizations can be difficult, in terms of efficiency and to guarantee that the solution is a global minimum. Recently, a general class of objectives have been introduced, called induced regularized factor mo...

We present a simple mathematical model of glassy dynamics seen as a random walk in a directed weighted network of minima taken as a representation of the energy landscape. Our approach gives a broader perspective to previous studies focusing on particular examples of energy landscapes obtained by sampling energy minima and saddles of small systems. We point out how the relation between the ener...

Learning controllers based on dynamic programming require some means of storing arbitrary functions and finding global minima within cross sections of those functions. There are many general methods for learning and representing functions, including polynomials, multi-layer perceptrons with backpropagation, and radial basis functions, but these systems do not allow the minima to be found easily...

Themulticanonical ansatz is used to study variations in the energy landscape of a small peptide, Met-enkephalin, under a change from the ECEPP/2 force field to ECEPP/3. Local minima with energies up to 5 kcal/mol higher than the global minima are sampled and classified according to H-bridges and backbone angles. The distribution and relative weight for various temperatures of the minima are cal...