Adaptive extremal optimization by detrended fluctuation analysis

Global optimization is one of the key challenges in computational physics as several problems, e.g. protein structure prediction, the low-energy landscape of atomic clusters, detection of community structures in networks, or model-parameter fitting can be formulated as global optimization problems. Extremal optimization (EO) has become in recent years one particular, successful approach to the global optimization problem. As with almost all other global optimization approaches, EO is driven by an internal dynamics that depends crucially on one or more parameters. Recently, the existence of an optimal scheme for this internal parameter of EO was proven, so as to maximize the performance of the algorithm. However, this proof was not constructive, that is, one cannot use it to deduce the optimal parameter itself a priori. In this study we analyze the dynamics of EO for a test problem (spin glasses). Based on the results we propose an online measure of the performance of EO and a way to use this insight to reformulate the EO algorithm in order to construct optimal values of the internal parameter online without any input by the user. This approach will ultimately allow us to make EO parameter free and thus its application in general global optimization problems much more efficient.     

Quadratic spline-on-spline

Recently Dolezal and Tewarson [2], and Papamichael and Soares [3] have considered the cubic spline-on-spline for the purpose of the approximating the derivatives y⁽²⁾,y⁽³⁾, and y⁽⁴⁾. In this paper their ideas have been extended and the quadratic spline-on-spline has been established for the same purpose. This technique yields better results than the traditional process using a single quadratic spline.     

Solving variational inequalities by a modified projection method with an effective step-size

In this paper, we propose a new projection method for the solution of variational inequality problems. The method is simple, which uses only function evaluations and projections onto the feasible set. We adopt a new step-size rule and a new search direction in the new method. Under the mild conditions, we prove the proposed method is globally convergent. Preliminary numerical results are reported.     

The convergence of conjugate gradient method with nonmonotone line search

The conjugate gradient method is a useful and powerful approach for solving large-scale minimization problems. Liu and Storey developed a conjugate gradient method, which has good numerical performance but no global convergence under traditional line searches such as Armijo line search, Wolfe line search, and Goldstein line search. In this paper we propose a new nonmonotone line search for Liu-Storey conjugate gradient method (LS in short). The new nonmonotone line search can guarantee the global convergence of LS method and has a good numerical performance. By estimating the Lipschitz constant of the derivative of objective functions in the new nonmonotone line search, we can find an adequate step size and substantially decrease the number of functional evaluations at each iteration. Numerical results show that the new approach is effective in practical computation.     

Gauge invariance,charge conservation,and variational principles

We present new results on the correspondence between symmetries, conservation laws and variational principles for field equations in general non-abelian gauge theories. Our main result states that second order field equations possessing translational and gauge symmetries and the corresponding conservation laws are always derivable from a variational principle. We also show by the way of examples that the above result fails in general for third order field equations.     

The eigenvalue complementarity problem

In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming Problem with Complementarity Constraints and a Global Optimization Problem. A finite Reformulation–Linearization Technique (Rlt)-based tree search algorithm is introduced for processing the EiCP via the lattermost of these formulations. Computational experience is included to highlight the efficacy of the above formulations and corresponding techniques for the solution of the EiCP.     

Three-step iterations for nonlinear accretive operator equations

In this paper, we suggest and analyze a three-step iterative scheme for solving nonlinear strongly accretive operator equation Tx=f without continuous condition in a uniformly smooth Banach space. Our results include the Ishikawa, Mann and Noor iterations as special cases. The results presented in this paper improve and extend almost all the current results in the more general setting.     

Integro-differential equations of hyperbolic type with positive definite kernels

The main purpose of this work is to study the damping effect of memory terms associated with singular convolution kernels on the asymptotic behavior of the solutions of second order evolution equations in Hilbert spaces. For kernels that decay exponentially at infinity and possess strongly positive definite primitives, the exponential stability of weak solutions is obtained in the energy norm. It is also shown that this theory applies to several examples of kernels with possibly variable sign, and to a problem in nonlinear viscoelasticity.     

Some optimal bounds in the central limit theorem using zero biasing

The convergence rate in the central limit theorem (CLT) is investigated in terms of a wide class of probability metrics. Namely, optimal estimates for the proximity between a probability distribution and its zero bias transformation are derived. These new inequalities allow one to establish optimal rates of convergence in the CLT for sums of independent random variables with finite moments of order s, s∈(2,3], in terms of ideal metrics introduced by V.M. Zolotarev.     

On the convergence rate and some applications of regularized ranking algorithms

This paper studies the ranking problem in the context of the regularization theory that allows a simultaneous analysis of a wide class of ranking algorithms. Some of them were previously studied separately. For such ones, our analysis gives a better convergence rate compared to the reported in the literature. We also supplement our theoretical results with numerical illustrations and discuss the application of ranking to the problem of estimating the risk from errors in blood glucose measurements of diabetic patients.