Bayesian network learning algorithm based on unconstrained optimization and ant colony optimization

Structure learning of Bayesian networks is a wellresearched but computationally hard task.For learning Bayesian networks,this paper proposes an improved algorithm based on unconstrained optimization and ant colony optimization（U-ACO-B） to solve the drawbacks of the ant colony optimization（ACO-B）.In this algorithm,firstly,an unconstrained optimization problem is solved to obtain an undirected skeleton,and then the ACO algorithm is used to orientate the edges,thus returning the final structure.In the experimental part of the paper,we compare the performance of the proposed algorithm with ACO-B algorithm.The experimental results show that our method is effective and greatly enhance convergence speed than ACO-B algorithm.

GLOBAL COVERGENCE OF THE NON-QUASI-NEWTON METHOD FOR UNCONSTRAINED OPTIMIZATION PROBLEMS

In this paper, the non-quasi-Newton＇s family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton＇s family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.

New type of conjugate gradient algorithms for unconstrained optimization problems

Two new formulaes of the main parameter βk of the conjugate gradient method are presented, which respectively can be seen as the modifications of method HS and PRP. In comparison with classic conjugate gradient methods, the new methods take both available gradient and function value information. Furthermore, their modifications are proposed. These methods are shown to be global convergent under some assumptions. Numerical results are also reported.

Subspace Minimization Conjugate Gradient Method Based on Cubic Regularization Model for Unconstrained Optimization

Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.

An Improved Quasi-Newton Method for Unconstrained Optimization

We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.

Global Convergence of Curve Search Methods for Unconstrained Optimization

In this paper we propose a new family of curve search methods for unconstrained optimization problems, which are based on searching a new iterate along a curve through the current iterate at each iteration, while line search methods are based on finding a new iterate on a line starting from the current iterate at each iteration. The global convergence and linear convergence rate of these curve search methods are investigated under some mild conditions. Numerical results show that some curve search methods are stable and effective in solving some large scale minimization problems.

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

TESTING DIFFERENT CONJUGATE GRADIENT METHODS FOR LARGE-SCALE UNCONSTRAINED OPTIMIZATION

In this paper we test different conjugate gradient (CG) methods for solving large-scale unconstrained optimization problems. The methods are divided in two groups: the first group includes five basic CG methods and the second five hybrid CG methods. A collection of medium-scale and large-scale test problems are drawn from a standard code of test problems, CUTE. The conjugate gradient methods are ranked according to the numerical results. Some remarks are given.

NON-QUASI-NEWTON UPDATES FOR UNCONSTRAINED OPTIMIZATION

In this report we present some new numerical methods for unconstrained optimization. These methods apply update formulae that do not satisfy the quasi-Newton equation. We derive these new formulae by considering different techniques of approximating the objective function. Theoretical analyses are given to show the advantages of using non-quasi-Newton updates. Under mild conditions we prove that our new update formulae preserve global convergence properties. Numerical results are also presented.

A NEW FAMILY OF TRUST REGION ALGORITHMS FOR UNCONSTRAINED OPTIMIZATION

Trust region (TR) algorithms are a class of recently developed algorithms for nonlinear optimization. A new family of TR algorithms for unconstrained optimization, which is the extension of the usual TR method, is presented in this paper. When the objective function is bounded below and continuously, differentiable, and the norm of the Hesse approximations increases at most linearly with the iteration number, we prove the global convergence of the algorithms. Limited numerical results are reported, which indicate that our new TR algorithm is competitive.

A QUASI-NEWTON ALGORITHM WITHOUT CALCULATING DERIVATIVES FOR UNCONSTRAINED OPTIMIZATION

A new algorithm for unconstrained optimization is developed, by using the product form of the OCSSR1 update. The implementation is especially useful when gradient information is estimated by difference formulae. Preliminary tests show that new algorithm can perform well.

Unconstrained Optimization Reformulations of Equilibrium Problems

We generalize the D-gap function developed in the literature for variational inequalities to a general equilibrium problem （EP）. Through the D-gap function, the equilibrium problem is cast as an unconstrained minimization problem. We give conditions under which any stationary point of the D-gap function is a solution of EP and conditions under which it provides a global error bound for EP. Finally, these results are applied to box-constrained EP and then weaker conditions are established to obtain the desired results for box-constrained EP.

A New Restarting Adaptive Trust-Region Method for Unconstrained Optimization

In this paper,we present a new adaptive trust-region method for solving nonlinear unconstrained optimization problems.More precisely,a trust-region radius based on a nonmonotone technique uses an approximation of Hessian which is adaptively chosen.We produce a suitable trust-region radius;preserve the global convergence under classical assumptions to the first-order critical points;improve the practical performance of the new algorithm compared to other exiting variants.Moreover,the quadratic convergence rate is established under suitable conditions.Computational results on the CUTEst test collection of unconstrained problems are presented to show the effectiveness of the proposed algorithm compared with some exiting methods.

A NEW NONMONOTONE TRUST REGION ALGORITHM FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS

Based on the nonmonotone line search technique proposed by Gu and Mo （Appl. Math. Comput. 55, （2008） pp. 2158-2172）, a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio ρk for evaluating the trial step dk whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.

A randomized nonmonotone adaptive trust region method based on the simulated annealing strategy for unconstrained optimization

Purpose–The purpose of this paper is to employ stochastic techniques to increase efficiency of the classical algorithms for solving nonlinear optimization problems.Design/methodology/approach–The well-known simulated annealing strategy is employed to search successive neighborhoods of the classical trust region(TR)algorithm.Findings–An adaptive formula for computing the TR radius is suggested based on an eigenvalue analysis conducted on the memoryless Broyden-Fletcher-Goldfarb-Shanno updating formula.Also,a(heuristic)randomized adaptive TR algorithm is developed for solving unconstrained optimization problems.Results of computational experiments on a set of CUTEr test problems show that the proposed randomization scheme can enhance efficiency of the TR methods.Practical implications–The algorithm can be effectively used for solving the optimization problems which appear in engineering,economics,management,industry and other areas.Originality/value–The proposed randomization scheme improves computational costs of the classical TR algorithm.Especially,the suggested algorithm avoids resolving the TR subproblems for many times.

A Regularized Newton Method with Correction for Unconstrained Convex Optimization

In this paper, we present a regularized Newton method (M-RNM) with correction for minimizing a convex function whose Hessian matrices may be singular. At every iteration, not only a RNM step is computed but also two correction steps are computed. We show that if the objective function is LC2, then the method posses globally convergent. Numerical results show that the new algorithm performs very well.

A NEW DERIVATIVE FREE OPTIMIZATION METHOD BASED ON CONIC INTERPOLATION MODEL

In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.

A New Subdivision Algorithm for the Bernstein Polynomial Approach to Global Optimization

In this paper, an improved algorithm is proposed for unconstrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems. The proposed algorithm is based on the Bernstein polynomial approach. Novel features of the proposed algorithm are that it uses a new rule for the selection of the subdivision point, modified rules for the selection of the subdivision direction, and a new acceleration device to avoid some unnecessary subdivisions. The performance of the proposed algorithm is numerically tested on a collection of 16 test problems. The results of the tests show the proposed algorithm to be superior to the existing Bernstein algorithm in terms of the chosen performance metrics.

Chaotic Aquila Optimization Algorithm for Solving Phase Equilibrium Problems and Parameter Estimation of Semi-empirical Models

This research study aims to enhance the optimization performance of a newly emerged Aquila Optimization algorithm by incorporating chaotic sequences rather than using uniformly generated Gaussian random numbers.This work employs 25 different chaotic maps under the framework of Aquila Optimizer.It considers the ten best chaotic variants for performance evaluation on multidimensional test functions composed of unimodal and multimodal problems,which have yet to be studied in past literature works.It was found that Ikeda chaotic map enhanced Aquila Optimization algorithm yields the best predictions and becomes the leading method in most of the cases.To test the effectivity of this chaotic variant on real-world optimization problems,it is employed on two constrained engineering design problems,and its effectiveness has been verified.Finally,phase equilibrium and semi-empirical parameter estimation problems have been solved by the proposed method,and respective solutions have been compared with those obtained from state-of-art optimizers.It is observed that CH01 can successfully cope with the restrictive nonlinearities and nonconvexities of parameter estimation and phase equilibrium problems,showing the capabilities of yielding minimum prediction error values of no more than 0.05 compared to the remaining algorithms utilized in the performance benchmarking process.

A modified three–term conjugate gradient method with sufficient descent property

A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.