Local Minimization Method Research Articles

Improving the Giant-Armadillo Optimization Method

Global optimization is widely adopted presently in a variety of practical and scientific problems. In this context, a group of widely used techniques are evolutionary techniques. A relatively new evolutionary technique in this direction is that of Giant-Armadillo Optimization, which is based on the hunting strategy of giant armadillos. In this paper, modifications to this technique are proposed, such as the periodic application of a local minimization method as well as the use of modern termination techniques based on statistical observations. The proposed modifications have been tested on a wide series of test functions available from the relevant literature and compared against other evolutionary methods.

Predicting Protein-Peptide Complex Structures by Accounting for Peptide Flexibility and the Physicochemical Environment.

Predicting protein-peptide complex structures is crucial to the understanding of a vast variety of peptide-mediated cellular processes and to peptide-based drug development. Peptide flexibility and binding mode ranking are the two major challenges for protein-peptide complex structure prediction. Peptides are highly flexible molecules, and therefore, brute-force modeling of peptide conformations of interest in protein-peptide docking is beyond current computing power. Inspired by the fact that the protein-peptide binding process is like protein folding, we developed a novel strategy, named MDockPeP2, which tries to address these challenges using physicochemical information embedded in abundant monomeric proteins with an exhaustive search strategy, in combination with an integrated global search and a local flexible minimization method. Only the peptide sequence and the protein crystal structure are required. The method was systemically assessed using a newly constructed structural database of 89 nonredundant protein-peptide complexes with the peptide sequence length ranging from 5 to 29 in which about half of the peptides are longer than 15 residues. MDockPeP2 yielded a total success rate of 58.4% (70.8, 79.8%) for the bound docking (i.e., with the bound receptor and fully flexible peptides) and 19.0% (44.8, 70.7%) for the challenging unbound docking when top 10 (100, 1000) models were considered for each prediction. MDockPeP2 achieved significantly higher success rates on two other datasets, peptiDB and LEADS-PEP, which contain only short- and medium-size peptides (≤ 15 residues). For peptiDB, our method obtained a success rate of 62.0% for the bound docking and 35.9% for the unbound docking when the top 10 models were considered. For LEADS-PEP, MDockPeP2 achieved a success rate of 69.8% when the top 10 models were considered. The program is available at https://zougrouptoolkit.missouri.edu/mdockpep2/download.html.

Assessment of Optimization Methods Used to Determine Plasticity Parameters Based on DIC and back Calculation Methods

In this paper, we analyse various minimization algorithms applied to the problem of determining elasto-plastic material parameters using an inverse analysis and digital image correlation (DIC) system. As the DIC system, ARAMIS is used, while for the finite element solution of boundary value problems, Abaqus software is applied. Different minimization algorithms, implemented in the SciPy Python library, were initially juxtaposed, compared and evaluated based on benchmark functions. Next the proper evaluation of the algorithms was performed to determine the material parameters for isotropic metal plasticity with the Huber-Mises yield criterion and isotropic or combined kinematic-isotropic plastic hardening models. For all researchers utilizing back calculation methods based on a DIC measuring system, such analysis results may be interesting. It was concluded that among the local minimization methods, derivative free optimization algorithms, especially the Powell algorithm, perform the most efficiently.

Solving Unconstrained Global Optimization Problem Using Parameter Free Filled Function in Cooperation with Jameson Gradient Based Method

Global optimization problem still becomes a challenges due to the problem on locating the global optimum of multimodal function. How to reach the better minimizer from the current minimizer and how to decide that the obtained minimizer is the desired one are both major challenges on solving global optimization problem. Filled function method is one of the recent considered deterministic easy applied methods which concerned to the mentioned problems. The basic concept of filled function method is firstly by minimizing the objective function (first phase) then to build such an auxiliary function which to be minimized (second phase) in order to locate a point with lower function value than the current minimizer of the objective function. In the second phase, a local minimization method can be applied. Newton’s method is considered to be fast method on finding the zero of gradient of quadratic function, but may be very expensive or infeasible to determine the Hessian matrix in the case of complex problems. The Jameson gradient based method is the search procedures which avoid the need to store an estimate of the Hessian as well as its inverse and do not require exact line searches. In this paper, an algorithm in cooperation of parameter free filled function method and Jameson gradient method are introduced for solving global optimization problem with two variables. The algorithm is implemented to some benchmark test function. The numerical performance of the method on solving two-dimensional global optimization problems is presented.

Evaluating the peptide structure prediction capabilities of a purely ab-initio method.

DEEPSAM is a relatively new global optimization algorithm aimed to predict the structure of bio-molecules from sequence, without any additional preliminary assumption. It is an evolutionary algorithm whose mutation operators are built by hybridizing the diffusion equation method, molecular dynamics simulated annealing, and a quasi-Newton local minimization method. The goal of this study was to evaluate the structure prediction capabilities of DEEPSAM by running it upon NMR structures of linear peptides (10-20 residues). The results indicate that DEEPSAM successfully predicted the conformations of these peptides, using modest computing resources.

Local risk minimization for vulnerable European contingent claims on nontradable assets under regime switching models

ABSTRACTThis article focuses on an optimal hedging problem of the vulnerable European contingent claims. The underlying asset of the vulnerable European contingent claims is assumed to be nontradable. The interest rate, the appreciation rate and the volatility of risky assets are modulated by a finite-state continuous-time Markov chain. By using the local risk minimization method, we obtain an explicit closed-form solution for the optimal hedging strategies of the vulnerable European contingent claims. Further, we consider a problem of hedging for a vulnerable European call option. Optimal hedging strategies are obtained. Finally, a numerical example for the optimal hedging strategies of the vulnerable European call option in a two-regime case is provided to illustrate the sensitivities of the hedging strategies.

Hedging of contingent claims written on non traded assets under Markov-modulated models

ABSTRACTThis paper studies the hedging problem of European contingent claims when the underlying asset is non traded. We assume that the share prices of the assets are governed by Markov-modulated processes; that is, the market parameters switch over the time according to a finite-state continuous time Markov chain. Due to the presence of Markov chain the non traded asset, the market which we consider is incomplete, we shall use the local risk minimization method to obtain an optimal hedging strategy in a closed-form for an investor. Finally, numerical illustrations of an optimal hedging strategy are given by the Monte Carlo simulation.

Pricing and hedging catastrophe equity put options under a Markov-modulated jump diffusion model

In this paper, we consider pricing and hedging of catastrophe equity put options undera Markov-modulated jump diffusion process with a Markov switching compensator. We assume that the risk free interest rate,the appreciation rate and the volatility of the risky asset depend on a finite-state Markov chain. We investigate the pricing of catastrophe equity put options and obtain the explicit pricing formulas. A numerical analysis is provided toillustrate the effect of regime switching on the price of catastrophe equity put options. In the end, since the market which we consider is not complete, we also provide an optimal hedging strategy by using the local risk minimization method.

L 1 C 1 polynomial spline approximation algorithms for large data sets

In this article, we address the problem of approximating data points by C 1-smooth polynomial spline curves or surfaces using L 1-norm. The use of this norm helps to preserve the data shape and it reduces extraneous oscillations. In our approach, we introduce a new functional which enables to control directly the distance between the data points and the resulting spline solution. The computational complexity of the minimization algorithm is nonlinear. A local minimization method using sliding windows allows to compute approximation splines within a linear complexity. This strategy seems to be more robust than a global method when applied on large data sets. When the data are noisy, we iteratively apply this method to globally smooth the solution while preserving the data shape. This method is applied to image denoising.

Doubly periodic self-dual vortices in a relativistic non-Abelian Chern–Simons model

In this paper we establish a multiplicity result concerning the existence of doubly periodic solutions for a $2\times2$ nonlinear elliptic system arising in the study of self-dual non-Abelian Chern--Simons vortices. We show that the given system admits at least two solutions when the Chern--Simons coupling parameter $\kappa>0$ is sufficiently small; while no solutions exist for $\kappa>0$ sufficiently large. As in [36] we use a variational formulation of the problem. Thus, we obtain a first solution via a (local) minimization method and show that it is asymptotically gauge-equivalent to the (broken) principal embedding vacuum of the system, as $\kappa\to 0$. Then we obtain the second solution by a min-max procedure of "mountain pass" type.

Risk-minimizing portfolio selection for insurance payment processes under a Markov-modulated model

This paper extends the model in Riesner (2007) to a Markov modulated Lévy process. The parameters of the Lévy process switch over time according to the different states of an economy, which is described by a finite-state continuous time Markov chain. Employing the local risk minimization method, we find an optimal hedging strategy for a general payment process. Finally, we give anexample for single unit-linked insurance contracts with guarantee todisplay the specific locally risk-minimizing hedging strategy.

Geometry Optimization of Atomic Clusters Using a Heuristic Method with Dynamic Lattice Searching

In this paper, a global optimization method is presented to determine the global-minimum structures of atomic clusters, where several already existing techniques are combined, such as the dynamic lattice searching method and two-phase local minimization method. The present method is applied to some selected large-sized Lennard-Jones (LJ) clusters and silver clusters described by the Gupta potential in the size range N = 13-140 and 300. Comparison with the results reported in the literature shows that the method is highly efficient and a lot of new global minima missed in previous papers are found for the silver clusters. The method may be a promising tool for the theoretical determination of ground-state structure of atomic clusters. Additionally, the stabilities of silver clusters are also analyzed and it is found that in the size range N = 13-140 there exist 12 particularly stable clusters.

Fast [formula omitted] polynomial spline interpolation algorithm with shape-preserving properties

In this article, we address the problem of interpolating data points by regular L 1 -spline polynomial curves of smoothness C k , k ⩾ 1 , that are invariant under rotation of the data. To obtain a C 1 cubic interpolating curve, we use a local minimization method in parallel on five data points belonging to a sliding window. This procedure is extended to create C k -continuous L 1 splines, k ⩾ 2 , on larger windows. We show that, in the C k -continuous ( k ⩾ 1 ) interpolation case, this local minimization method preserves the linear parts of the data well, while a global L 1 minimization method does not in general do so. The computational complexity of the procedure is linear in the global number of data points, no matter what the order C k of smoothness of the curve is.

A new filled function method for nonlinear equations

In this paper, a new global optimization approach based on the filled function method is proposed for solving box-constrained systems of nonlinear equations. We first convert the nonlinear system into an equivalent global optimization problem, and then propose a new filled function method to solve the converted global optimization problem. Several numerical examples are presented and solved by using different local minimization methods, which illustrate the efficiency of the present approach.

Risk minimization under budget constraints

PurposeThe purpose of this paper is to find the optimal hedging strategy when an investor has budget constraints on both the initial capital and the future cash flow.Design/methodology/approachThe paper follows the utility minimization of the total cost, using convex utility functions on both initial capital and future cash flows.FindingsClosed‐form solutions of optimal hedging strategies are found in some specific but popular cases. It is also found that this method corresponds to the local risk minimization method in quadratic hedging.Research limitations/implicationsHedging strategies are calculated for only two popular choices. One may want to calculate hedging strategies for other popular utility functions such as power utility or HARA utility.Practical implicationsWhen a trader has some budget constraint in both initial capital and future cash flows, this paper gives a simple alternative.Originality/valueBudget constraints on both initial capital and future cash flow are new to this kind of study. Connection to the local risk minimization strategy is original too.

Insiders' hedging in a jump diffusion model

In this paper, we formulate the optimal hedging problem when the underlying stock price has jumps, especially for insiders who have more information than the general public. The jumps in the underlying price process depend on another diffusion process, which models a sequence of firm-specific information. This diffusion process is observed only by insiders. Nevertheless, the market is incomplete to insiders as well as to the general public. We use the local risk minimization method to find an optimal hedging strategy for insiders. We also numerically compare the value of the insider's hedging portfolio with the value of an honest trader's hedging portfolio for a simulated sample path of a stock price.

Discrete hedging of American-type options using local risk minimization

Local risk minimization and total risk minimization discrete hedging have been extensively studied for European options [e.g., Schweizer, M., 1995. Variance-optimal hedging in discrete time. Mathematics of Operation Research 20, 1–32; Schweizer, M., 2001. A guided tour through quadratic hedging approaches. In: Jouini, E., Cvitanic, J., Musiela, M., Option pricing, interest rates and risk management, Cambridge University Press, pp. 538–574]. In practice, hedging of options with American features is more relevant. For example, equity linked variable annuities provide surrender benefits which are essentially embedded American options. In this paper we generalize both quadratic and piecewise linear local risk minimization hedging frameworks to American options. We illustrate that local risk minimization methods outperform delta hedging when the market is highly incomplete. In addition, compared to European options, distributions of the hedging costs are typically more skewed and heavy-tailed. Moreover, in contrast to quadratic local risk minimization, piecewise linear risk minimization hedging strategies can be significantly different, resulting in larger probabilities of small costs but also larger extreme cost.

Application of the simplex simulated annealing technique to nonlinear parameter optimization for the SAFT-VR equation of state

A non-equilibrium simplex simulated annealing algorithm is applied as a global optimization method to parameter optimization for an equation of state based on the generalized statistical associating fluid theory incorporating potentials of variable range. The parameters are determined by optimizing the calculated phase behaviour of a number of pure solvents, such as water and alcohols, and aqueous electrolyte solutions. The optimized parameters obtained via the simulated annealing algorithm are compared to those obtained using the simplex method and, for the electrolyte solutions, a gradient-based quasi-Newton method. In the case of the pure solvents, the lowest values of the objective function have been obtained using the simulated annealing technique in six out of the seven studied systems, while for the electrolyte solutions the method results in the lowest values in nine systems out of 11; in the other systems the local methods have resulted in lower values of the objective function. It is observed that both for the solvents and the solutions considered the parameters obtained using the annealing technique are theoretically justifiable, follow physically meaningful trends, and can more easily be generalized; such results provide a measure of confidence that the annealing method does converge to the global minimum in the majority of the studied systems. For pure solvents a simple generalization of parameters leads to accurate predictions for other solvents in the same homologous series. In the case of the electrolyte systems correlations among parameters obtained via simulated annealing can be qualitatively identified, and a simple correlation is proposed which simplifies the molecular models. This is generally not the case for the two local minimization methods considered which, except for a few specific cases, lead to parameters showing no general trends, despite the calculated phase behaviour being almost identical.

GLOBAL CONFORMATION OPTIMIZATION OF MIXED CLUSTERS USING A GENETIC ALGORITHM

The genetic algorithm (M. Iwamatsu, J. Chem. Phys.112, 10976 (2000)), which combines the space-fixed genetic algorithm of Niesse and Mayne (J. Chem. Phys.105, 4700 (1996)) with simplex local minimization method is generalized to handle the conformation optimization of binary mixed clusters. This genetic algorithm based on real coding can successfully find the lowest energy structure of mixed argon–xenon alloys Ar x Xe 13-x and confirms the results found by other methods.

532 ランダムパターンを用いた高精度画像相関法の開発

In order to measure the displacement distributions on material surfaces, many types of image correlation method have been developed in various research fields. In this study, to measure highly accurate displacement field near a crack tip, the local correlation minimization method is proposed based on the image correlation scheme. First, the formulations of the image correlation and the local correlation minimization method are explained in this paper. Then, the corroboration of the local correlation minimization method is carried out by the measuring a known analytical near tip field under mixed-mode loading.