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Solving nonlinear optimization Problems of Real Functions in Complex Variables by Complex-Valued Iterative Methods

IEEE TRANSACTIONS ON CYBERNETICS 2018年第1期48卷 277-287页

作者： Zhang, Songchuan Xia, Youshen Fuzhou Univ Ctr Discrete Math & Theoret Comp Sci Fuzhou 350116 Fujian Peoples R China Minjiang Univ Dept Math Fuzhou 350108 Fujian Peoples R China Fuzhou Univ Coll Math & Comp Sci Fuzhou Fujian Peoples R China

Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an l(1)-norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.

关键词： constrained nonlinear optimization complex variables complex-valued iteration method convergence analysis

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A penalty-based algorithm proposal for engineering optimization problems

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NEURAL COMPUTING & APPLICATIONS 2023年第10期35卷 7635-7658页

作者： Oztas, Gulin Zeynep Erdem, Sabri Pamukkale Univ Dept Business Adm TR-20160 Denizli Turkey Dokuz Eylul Univ Dept Business TR-35390 Izmir Turkey

This paper presents a population-based evolutionary computation model for solving continuous constrained nonlinear optimization problems. The primary goal is achieving better solutions in a specific problem type, regardless of metaphors and similarities. The proposed algorithm assumes that candidate solutions interact with each other to have better fitness values. The interaction between candidate solutions is limited with the closest neighbors by considering the Euclidean distance. Furthermore, Tabu Search Algorithm and Elitism selection approach inspire the memory usage of the proposed algorithm. Besides, this algorithm is structured on the principle of the multiplicative penalty approach that considers satisfaction rates, the total deviations of constraints, and the objective function value to handle continuous constrained problems very well. The performance of the algorithm is evaluated with real-world engineering design optimization benchmark problems that belong to the most used cases by evolutionary optimization researchers. Experimental results show that the proposed algorithm produces satisfactory results compared to the other algorithms published in the literature. The primary purpose of this study is to provide an algorithm that reaches the best-known solution values rather than duplicating existing algorithms through a new metaphor. We constructed the proposed algorithm with the best combination of features to achieve better solutions. Different from similar algorithms, constrained engineering problems are handled in this study. Thus, it aims to prove that the proposed algorithm gives better results than similar algorithms and other algorithms developed in the literature.

关键词： Natural facts Evolutionary computation constrained nonlinear optimization Engineering benchmark problems Metaheuristics Nature-inspired optimization algorithms

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A robust method for image stitching

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PATTERN ANALYSIS AND APPLICATIONS 2021年第4期24卷 1847-1858页

作者： Pellikka, Matti Lahtinen, Valtteri Grundium Ltd Hermiankatu 6-8G Tampere 33720 Finland Aalto Univ QTF Ctr Excellence Dept Appl Phys QCD Labs Aalto 00076 Finland

We propose a novel method for large-scale image stitching that is robust against repetitive patterns and featureless regions in the imagery. In such cases, state-of-the-art image stitching methods easily produce image alignment artifacts, since they may produce false pairwise image registrations that are in conflict within the global connectivity graph. Our method augments the current methods by collecting all the plausible pairwise image registration candidates, among which globally consistent candidates are chosen. This enables the stitching process to determine the correct pairwise registrations by utilizing all the available information from the whole imagery, such as unambiguous registrations outside the repeating pattern and featureless regions. We formalize the method as a weighted multigraph whose nodes represent the individual image transformations from the composite image, and whose sets of multiple edges between two nodes represent all the plausible transformations between the pixel coordinates of the two images. The edge weights represent the plausibility of the transformations. The image transformations and the edge weights are solved from a non-linear minimization problem with linear constraints, for which a projection method is used. As an example, we apply the method in a large-scale scanning application where the transformations are primarily translations with only slight rotation and scaling component. Despite these simplifications, the state-of-the-art methods do not produce adequate results in such applications, since the image overlap is small, which can be featureless or repetitive, and misalignment artifacts and their concealment are unacceptable.

关键词： Image stitching Image registration Image mosaic constrained nonlinear optimization

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Multi-item EOQ model with nonlinear unit holding cost and partial backordering: moth-flame optimization algorithm

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2017年第1期34卷 42-51页

作者： Khalilpourazari, Soheyl Pasandideh, Seyed Hamid Reza Kharazmi Univ Dept Ind Engn Fac Engn Tehran Iran

In this paper, a multi-item multi-constrained Economic Order Quantity model with nonlinear unit holding cost and partial backordering is proposed. To develop an applicable model, different technical, physical, and strategic constraints are considered such as available budget, warehouse capacity, total permissible holding cost, and total permissible backordering cost constraints. The goal is to determine the lengths of inventory cycles, where the inventory level is positive and negative such that the total inventory costs are minimized. In addition, backordering rate during shortage period for each product is considered as a decision variable which can significantly reduce the total inventory costs. Due to complexity and nonlinearity of the proposed model, interior-point method and Moth-Flame optimization algorithm are utilized to solve the model in different sizes. At the end, the performance of the solution methods is compared statistically considering three measures to determine the superior solution method.

关键词： Economic order quantity moth-flame optimization algorithm partial backordering nonlinear unit holding cost interior-point method constrained nonlinear optimization

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On the estimation of nonlinearly aggregated mixed models

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2006年第1期15卷 18-38页

作者： Proietti, T Univ Roma Tor Vergata SEF&ME Q I-00133 Rome Italy

The article proposes an iterative algorithm for the estimation of fixed and random effects of a nonlinearly aggregated mixed model. The latter arises when an additive Gaussian model is formulated at the disaggregate level on a nonlinear transformation of the responses, but information is available in aggregate form. The nonlinear transformation breaks the linearity of the aggregate model, yielding a nonlinear tight observational constraint. The algorithm rests upon the sequential linearization of the nonlinear aggregation constraint around proposals that are iteratively updated until convergence. Two alternative pseudo maximum likelihood methods are discussed and compared. As a byproduct we provide a solution to the problem of distributing the aggregate responses over the units of analysis, enforcing the nonlinear observational constraints. Illustrations referring to the temporal disaggregation problem are provided.

关键词： best linear unbiased prediction Box-Cox transformation constrained nonlinear optimization temporal and spatial disaggregation

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Practical image fusion method based on spectral mixture analysis

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Science China(Information Sciences) 2010年第6期53卷 1277-1286页

作者： MATSUSHITA Bunkei Department of Geography University of Tsukuba

Conventional image fusion algorithm, such as IHS, SVR, PCS, etc., may show some defects in inheriting the higher-spectral information embedded in the original lower-spatial resolution MS image.A fusion method based on spectral mixture analysis(FSMA) was proposed in previous study, which has potential in solving this *** published results are limited to well-behaved simulated data where the endmembers are known a priori and the FSMA method will not work well when applying to real remotely sensed images because the estimated reflectance ranging in panchromatic band derived from MS bands cannot be treated as the real panchromatic *** this paper, an improved image fusion method based on spectral mixture analysis(IFSMA) is proposed, in which the original FSMA method was extended to real remotely sensed images by modifying the objective function of the constrained nonlinear optimization *** was compared with the original FSMA, Zhang’s SVR, PCS and IHS method, and results indicated that the IFSMA method was superior to other methods in preserving the spectral and spatial information.

关键词： image fusion spectral mixture analysis constrained nonlinear optimization

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MAXIMUM-LIKELIHOOD ESTIMATION OF UNIMODAL AND DECREASING DENSITIES BASED ON ARBITRARILY RIGHT-CENSORED DATA

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COMMUNICATIONS IN STATISTICS PART A-THEORY AND METHODS 1982年第20期11卷 2259-2270页

作者： MCNICHOLS, DT PADGETT, WJ Department of Mathematics and Statistics University of South Carolina Columbia South Carolina 29208 United States

Nonparametric maximum likelihood estimation of decreasing and unimodal density functions based on observations subject to arbitrary right censorship is considered. The maximum likelihood estimator of both types of densities is shown to exist and is a step function. The estimators may be computed for small samples by maximizing nonlinear equations subject to linear constraints, and the SUMT algorithm for constrained nonlinear optimization is used for the necessary calculations in an example.

关键词： nonparametric estimation survival function estimati constrained nonlinear optimization density estimation random censorship Kaplan-Meier estimator

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An optimal approximation of the characteristics of the GI/M/1 queue with two-stage service policy

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OPERATIONAL RESEARCH 2020年第2期20卷 959-983页

作者： Cherfaoui, Mouloud Bareche, Aicha Univ Bejaia Res Unit LaMOS Modeling & Optimizat Syst Bejaia 06000 Algeria Univ Biskra Dept Math Biskra 07000 Algeria

In this paper, we consider an GI/M/1 system with two-stage service policy, having a service rate (mu 1,mu 2), for which we determine its global transition operator. After that, with using the strong stability method we establish the approximation conditions for the stationary characteristics of this system by those of the standard GI/M/1 system. Under assumption that the approximation conditions are satisfied, we give the estimate of the deviation (stability inequalities) between the stationary distribution of the GI/M/1 system with two-stage service policy and those of the standard GI/M/1 system for three considered cases: the standard system has a service rate mu 1 (minimal threshold policy), the standard system has a service rate mu 2\ (maximal threshold policy) and the standard system has a service rate mu* minimizing the deviation (optimal policy). To calculate these deviations, the situation is modeled by a mathematical optimization problem which belongs to the minimization of a constrained nonlinear multi-variable function. Finally, numerical studies are performed to support the theoretical obtained results.

关键词： Hysteretic queue Markov chain Perturbation Approximation Strong stability constrained nonlinear optimization

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Optimal weighted Bonferroni tests and their graphical extensions

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STATISTICS IN MEDICINE 2024年第3期43卷 475-500页

作者： Xi, Dong Chen, Yao Gilead Sci Foster City CA 94404 USA Novartis Pharmaceut E Hanover NJ USA

Regulatory guidelines mandate the strong control of the familywise error rate in confirmatory clinical trials with primary and secondary objectives. Bonferroni tests are one of the popular choices for multiple comparison procedures and are building blocks of more advanced procedures. It is usually of interest to find the optimal weighted Bonferroni split for multiple hypotheses. We consider two popular quantities as the optimization objectives, which are the disjunctive power and the conjunctive power. The former is the probability to reject at least one false hypothesis and the latter is the probability to reject all false hypotheses. We investigate the behavior of each of them as a function of different Bonferroni splits, given assumptions about the alternative hypotheses and correlations between test statistics. Under independent tests, unique optimal Bonferroni weights exist;under dependence, optimal Bonferroni weights may not be unique based on a fine grid search. In general, we propose an optimization algorithm based on constrained nonlinear optimization and multiple starting points. The proposed algorithm efficiently identifies optimal Bonferroni weights to maximize the disjunctive or conjunctive power. In addition, we apply the proposed algorithm to graphical approaches, which include many Bonferroni-based multiple comparison procedures. Utilizing the closed testing principle, we adopt a two-step approach to find optimal graphs using the disjunctive power. We also identify a class of closed test procedures that optimize the conjunctive power. We apply the proposed algorithm to a case study to illustrate the utility of optimal graphical approaches that reflect study objectives.

关键词： Bonferroni test conjunctive power constrained nonlinear optimization disjunctive power family-wise error rate graphical approach

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Numerical experience with a derivative-free trust-funnel method for nonlinear optimization problems with general nonlinear constraints

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optimization METHODS & SOFTWARE 2016年第3期31卷 511-534页

作者： Sampaio, Ph. R. Toint, Ph. L. Univ Namur Namur Ctr Complex Syst naXys 61 Rue Bruxelles B-5000 Namur Belgium Univ Namur Dept Math 61 Rue Bruxelles B-5000 Namur Belgium

A trust-funnel method is proposed for solving nonlinear optimization problems with general nonlinear constraints. It extends the one presented by Gould and Toint [nonlinear programming without a penalty function or a filter. Math. Prog. 122(1):155-196, 2010], originally proposed for equality-constrained optimization problems only, to problems with both equality and inequality constraints and where simple bounds are also considered. As the original one, our method makes use of neither filter nor penalty functions and considers the objective function and the constraints as independently as possible. To handle the bounds, an active-set approach is employed. We then exploit techniques developed for derivative-free optimization (DFO) to obtain a method that can also be used to solve problems where the derivatives are unavailable or are available at a prohibitive cost. The resulting approach extends the DEFT-FUNNEL algorithm presented by Sampaio and Toint [A derivative-free trust-funnel method for equality-constrained nonlinear optimization. Comput. Optim. Appl. 61(1):25-49, 2015], which implements a derivative-free trust-funnel method for equality-constrained problems. Numerical experiments with the extended algorithm show that our approach compares favourably to other well-known model-based algorithms for DFO.

关键词： constrained nonlinear optimization trust-region method trust funnel derivative-free optimization

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