Adaptive State-Dependent Diffusion for Derivative-Free Optimization

This paper develops and analyzes a stochastic derivative-free optimization strategy.A key feature is the state-dependent adaptive variance.We prove global convergence in probability with algebraic rate and give the quantitative results in numerical examples.A striking fact is that convergence is achieved without explicit information of the gradient and even without comparing different objective function values as in established methods such as the simplex method and simulated annealing.It can otherwise be compared to annealing with state-dependent temperature.

解决非线性互补问题的Derivative-Free算法

基于NCP(F)的约束极小化变形,构造了一种新的merit函数,将原始的NCP(F)问题转化为约束极小化问题,并构造了相应的derivative-free下降算法,并在merit函数严格单调的条件下证明了derivative-free算法的合理性以及整体收敛性.

基于滤子技术的非线性互补问题的Derivative-Free算法

由于滤子技术有很高的应用价值,并能得到很好的数值结果,近来滤子法被广泛用来处理非线性规划问题.论文提出了一种新的解决非线性互补问题的Derivative-Free滤子算法,该算法在单调性的假设下能全局收敛于非线性互补问题的解.

一种新的求解非线性互补问题的Derivative-Free算法

把NCP(F)通过约束极小化变形转化为无约束极小化问题,构造一种新的D eriva-tive-F ree下降算法,并在一定条件下证明了D erivative-F ree下降算法的合理性及整体收敛性。

非线性互补问题的Derivative-Free下降方法

基于非线性互补问题(N CP(F))的约束极小化变形,构造一种新的m erit函数,将原始的N CP(F)问题转化为约束极小化问题,构造相应的derivative-free下降算法.在m erit函数严格单调的条件下证明derivative-free下降算法的合理性以及整体收敛性.

Identification of the unknown shielding parameters with gammaray spectrum using a derivative-free inverse radiation transport model

Identifying the unknown geometric and material information of a multi-shield object by analyzing the radiation signature measurements is always an important problem in national and global security. In order to identify the unknown shielding layer thicknesses of a source/shield system with gamma-ray spectra, we have developed a derivative-free inverse radiation transport model based on a differential evolution algorithm with global and local neighbourhoods(IRT-DEGL). In the present paper, the IRT-DEGL model is further extended for estimating the unknown thicknesses with random initial guesses and material mass densities of multi-shielding layers as well as their combinations. Using the detected gamma-ray spectra,the illustration of inverse studies is implemented and the main influence factors for inverse results are also analyzed.

非线性互补问题的一种改进Derivative-free下降方法

提出了一种改进的用于求解非线性互补问题Derivative-free下降方法,其搜索方向为罚Fischer-Burmeister函数非负偏导数的凸组合,搜索策略为一类新的非单调搜索。证明了该算法具有全局收敛性,与传统的Derivative-free下降方法相比,提高了收敛速率,减少了迭代次数。

Constructive Theory of Designing Optimal Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations

This paper stresses the theoretical nature of constructing the optimal derivative-free iterations. We give necessary and sufficient conditions for derivative-free three-point iterations with the eighth-order of convergence. We also establish the connection of derivative-free and derivative presence three-point iterations. The use of the sufficient convergence conditions allows us to design wide class of optimal derivative-free iterations. The proposed family of iterations includes not only existing methods but also new methods with a higher order of convergence.

通信噪音条件下非光滑优化问题的分布式derivative-free方法

本文研究了时变有向图上的非光滑分布式优化.在这样的图中,网络拓扑不仅是强连通的,而且还存在通信噪音.每个节点只能访问其非平滑的局部成本函数.本文给出了一种derivative-free分布式方法来最小化该网络中所有节点的成本函数之和.然后建立了所提出方法的收敛性分析,并获得了收敛速度的显式复杂性界限.当每个局部成本函数都是凸的时,我们的分析表明,所提出的算法以■的速率收敛,收敛速率取决于噪声的上限、光滑参数以及网络信息传播速度和节点间不平衡影响.当每个局部成本函数fi是强凸时,我们得到了O(lnt/t)的更快的收敛速度.最后,用一个数值实验来展示所提出方法的收敛性.

A Derivative-Free Optimization Algorithm Combining Line-Search and Trust-Region Techniques

The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some conditions.The authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration step.They analyze the optimization dynamics and convergence of the algorithm SUSD-TR.Details of the trial step and structure step are given.Numerical results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD direction.Their algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.

Derivative-free reinforcement learning:a review

Reinforcement learning is about learning agent models that make the best sequential decisions in unknown environments.In an unknown environment,the agent needs to explore the environment while exploiting the collected information,which usually forms a sophisticated problem to solve.Derivative-free optimization,meanwhile,is capable of solving sophisticated problems.It commonly uses a sampling-andupdating framework to iteratively improve the solution,where exploration and exploitation are also needed to be well balanced.Therefore,derivative-free optimization deals with a similar core issue as reinforcement learning,and has been introduced in reinforcement learning approaches,under the names of learning classifier systems and neuroevolution/evolutionary reinforcement learning.Although such methods have been developed for decades,recently,derivative-free reinforcement learning exhibits attracting increasing attention.However,recent survey on this topic is still lacking.In this article,we summarize methods of derivative-free reinforcement learning to date,and organize the methods in aspects including parameter updating,model selection,exploration,and parallel/distributed methods.Moreover,we discuss some current limitations and possible future directions,hoping that this article could bring more attentions to this topic and serve as a catalyst for developing novel and efficient approaches.

On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure

In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly approximated.At each iteration,we construct a quadratic interpolation model of the objective function around the current iterate.The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region.The filter technique is used to ensure the feasibility and optimality of the iterative sequence.Global convergence of the proposed algorithm is proved under some suitable assumptions.

AN AFFINE SCALING DERIVATIVE-FREE TRUST REGION METHOD WITH INTERIOR BACKTRACKING TECHNIQUE FOR BOUNDED-CONSTRAINED NONLINEAR PROGRAMMING

This paper proposes an arlene scaling derivative-free trust region method with interior backtracking technique for bounded-constrained nonlinear programming. This method is designed to get a stationary point for such a problem with polynomial interpolation models instead of the objective function in trust region subproblem. Combined with both trust region strategy and line search technique, at each iteration, the affine scaling derivative-free trust region subproblem generates a backtracking direction in order to obtain a new accepted interior feasible step. Global convergence and fast local convergence properties are established under some reasonable conditions. Some numerical results are also given to show the effectiveness of the proposed algorithm.

Hybrid data-driven framework for shale gas production performance analysis via game theory, machine learning, and optimization approaches

A comprehensive and precise analysis of shale gas production performance is crucial for evaluating resource potential,designing a field development plan,and making investment decisions.However,quantitative analysis can be challenging because production performance is dominated by the complex interaction among a series of geological and engineering factors.In fact,each factor can be viewed as a player who makes cooperative contributions to the production payoff within the constraints of physical laws and models.Inspired by the idea,we propose a hybrid data-driven analysis framework in this study,where the contributions of dominant factors are quantitatively evaluated,the productions are precisely forecasted,and the development optimization suggestions are comprehensively generated.More specifically,game theory and machine learning models are coupled to determine the dominating geological and engineering factors.The Shapley value with definite physical meaning is employed to quantitatively measure the effects of individual factors.A multi-model-fused stacked model is trained for production forecast,which provides the basis for derivative-free optimization algorithms to optimize the development plan.The complete workflow is validated with actual production data collected from the Fuling shale gas field,Sichuan Basin,China.The validation results show that the proposed procedure can draw rigorous conclusions with quantified evidence and thereby provide specific and reliable suggestions for development plan optimization.Comparing with traditional and experience-based approaches,the hybrid data-driven procedure is advanced in terms of both efficiency and accuracy.

An Efficient Pattern Search Method

Pattern search algorithms is one of most frequently used methods which were designed to solve the derivative-free optimization problems. Such methods get growing need with the development of science, engineering, economy and so on. Inspired by the idea of Hooke and Jeeves, we introduced an integer m in the algorithm which controls the number of steps of iteration update. We mean along the descent direction to allow the algorithm to?go ahead m steps at most to explore whether we can get better solution further. The experiment proved the strategy’s efficiency.

Automatic Simulation of the Chemical Langevin Equation

Biochemical systems have important practical applications, in particular to understanding critical intra-cellular processes. Often biochemical kinetic models represent cellular processes as systems of chemical reactions, traditionally modeled by the deterministic reaction rate equations. In the cellular environment, many biological processes are inherently stochastic. The stochastic fluctuations due to the presence of some low molecular populations may have a great impact on the biochemical system behavior. Then, stochastic models are required for an accurate description of the system dynamics. An important stochastic model of biochemical kinetics is the Chemical Langevin Equation. In this work, we provide a numerical method for approximating the solution of the Chemical Langevin Equation, namely the derivative-free Milstein scheme. The method is compared with the widely used strategy for this class of problems, the Milstein method. As opposed to the Milstein scheme, the proposed strategy has the advantage that it does not require the calculation of exact derivatives, while having the same strong order of accuracy as the Milstein scheme. Therefore it may be used for an automatic simulation of the numerical solution of the Chemical Langevin Equation. The tests on several models of practical interest show that our method performs very well.

Channel Knowledge Map(CKM)-Assisted Multi-UAV Wireless Network:CKM Construction and UAV Placement

Channel knowledge map(CKM)has recently emerged as a viable new solution to facilitate the placement and trajectory optimization for unmanned aerial vehicle(UAV)communications,by exploiting the siteand location-specific radio propagation information.This paper investigates a CKM-assisted multi-UAV wireless network,by focusing on the construction and utilization of CKMs for multi-UAV placement optimization.First,we consider the CKM construction problem when data measurements for only a limited number of points are available.Towards this end,we exploit a data-driven interpolation technique,namely the Kriging method,to construct CKMs to characterize the signal propagation environments.Next,we study the multi-UAV placement optimization problem by utilizing the constructed CKMs,in which the multiple UAVs aim to optimize their placement locations to maximize the weighted sum rate with their respectively associated ground base stations(GBSs).However,the weighted sum rate function based on the CKMs is generally non-differentiable,which renders the conventional optimization techniques relying on function derivatives inapplicable.To tackle this issue,we propose a novel iterative algorithm based on derivative-free optimization,in which a series of quadratic functions are iteratively constructed to approximate the objective function under a set of interpolation conditions,and accordingly,the UAVs’placement locations are updated by maximizing the approximate function subject to a trust region constraint.Finally,numerical results are presented to validate the performance of the proposed designs.It is shown that the Kriging method can construct accurate CKMs for UAVs.Furthermore,the proposed derivative-free placement optimization design based on the Kriging-constructed CKMs achieves a weighted sum rate that is close to the optimal exhaustive search design based on ground-truth CKMs,but with much lower implementation complexity.In addition,the proposed design is shown to significantly outperform other benchmark schemes.

A GLOBALLY DERIVTIVE-FREE DESCENT METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS

Based on a class of functions, which generalize the squared Fischer-Burmeister NCP function and have many desirable properties as the latter function has, we reformulate nonlinear complementarity problem (NCP for short) as an equivalent unconstrained optimization problem, for which we propose a derivative-free de- scent method in monotone case. We show its global convergence under some mild conditions. If F, the function involved in NCP, is Ro-function, the optimization problem has bounded level sets. A local property of the merit function is discussed. Finally, we report some numerical results.