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An Interval Reduced Basis Approach and its Integrated Framework for Acoustic Response Analysis of Coupled Structural-Acoustic System

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JOURNAL OF COMPUTATIONAL ACOUSTICS 2017年第3期25卷 1750009-1750009页

作者： Lv, Zheng Qiu, Zhiping Li, Qi Beijing Univ Aeronaut & Astronaut Inst Solid Mech Beijing 100191 Peoples R China Chinese Acad Sci Shenyang Inst Automat State Key Lab Robot Shenyang 110016 Liaoning Peoples R China

An interval reduced basis approach (IRBA) is presented for analyzing acoustic response of coupled structural-acoustic system with interval parameters. Simultaneously an integrated framework based on IRBA is established to deal with uncertain acoustic propagation using deterministic finite element (FE) software. The present IRBA aims to improve the accuracy of the conventional first-order approximation and also allow the efficient calculation of second-order approximation of acoustic response. In IRBA, acoustic response is approximated using a linear combination of interval basis vectors with undetermined coefficients. To get explicit expression of acoustic response in terms of interval parameters, the three terms of the second-order perturbation method are employed as basis vectors, and the variant of the Galerkin scheme is applied for derivation of the reduced-order system of equations. For the second-order approximation, the determination of acoustic response interval is reformulated into a series of quadratic programming problems, which are solved using the difference of convex functions (dc) algorithm effectively. The performance of IRBA and availability of the present framework are validated by numerical examples.

关键词： Interval reduced basis approach integrated framework structural-acoustic system interval parameters quadratic programming problem dc algorithm

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Personalized Dose Finding Using Outcome Weighted Learning

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2016年第516期111卷 1509-1521页

作者： Chen, Guanhua Zeng, Donglin Kosorok, Michael R. Vanderbilt Univ Dept Biostat 221 Kirkland Hall Nashville TN 37235 USA Univ N Carolina Dept Biostat Chapel Hill NC 27599 USA Univ N Carolina Dept Stat Chapel Hill NC USA

In dose-finding clinical trials, it is becoming increasingly important to account for individual-level heterogeneity while searching for optimal doses to ensure an optimal individualized dose rule (IDR) maximizes the expected beneficial clinical outcome for each individual. In this article, we advocate a randomized trial design where candidate dose levels assigned to study subjects are randomly chosen from a continuous distribution within a safe range. To estimate the optimal IDR using such data, we propose an outcome weighted learning method based on a nonconvex loss function, which can be solved efficiently using a difference of convex functions algorithm. The consistency and convergence rate for the estimated IDR are derived, and its small-sample performance is evaluated via simulation studies. We demonstrate that the proposed method outperforms competing approaches. Finally, we illustrate this method using data from a cohort study for warfarin (an anti-thrombotic drug) dosing. Supplementary materials for this article are available online.

关键词： dc algorithm Dose finding Individualized dose rule Risk bound Weighted support vector regression

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An Interval-Reduced-Basis Approach for Predicting Acoustic Response of Coupled Structural-Acoustic System 5th

An Interval-Reduced-Basis Approach for Predicting Acoustic R...

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5th International Conference on Electrical Engineering and Automatic Control (ICEEAC)

作者： Lv, Zheng Qiu, Zhiping Li, Qi Beihang Univ Sch Aeronaut Sci & Engn Beijing 100191 Peoples R China

ISBN: (纸本)9783662487686;9783662487662

To predict and improve the acoustic behavior, an interval-reduced-basis approach is presented for acoustic response of coupled structural-acoustic system. In the present approach, the acoustic response is approximated by using a linear combination of interval-basis vectors with undetermined coefficients. The reduced-order equations are derived based on Galerkin scheme to compute the undetermined coefficients. In addition, the determination of the acoustic response range is transformed into a sequence of quadratic programming problems subject to box constraints, which are computed using the dc algorithm effectively. Numerical example is presented to demonstrate the implementation of the present approach and show that the new approach has a good accuracy and efficiency.

关键词： Interval-reduced-basis approach Acoustic response Coupled structural-acoustic system Quadratic programming problem dc algorithm

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Linear convergence of a type of iterative sequences in nonconvex quadratic programming

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2015年第2期423卷 1311-1319页

作者： Hoang Ngoc Tuan Hanoi Pedag Univ Dept Math Phuc Yen Vinh Phuc Vietnam

By using error bounds for affine variational inequalities we prove that any iterative sequence generated by the Projection dc (Difference-of-Convex functions) decomposition algorithm in quadratic programming is R-linearly convergent, provided that the original problem has solutions. Our result solves in the affirmative the first part of the conjecture stated by Le Thi, Pham Dinh and Yen in their recent paper [8, p. 489]. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Quadratic programming dc algorithm dcA sequence Convergence rate

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Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第1期164卷 234-245页

作者： Hoang Ngoc Tuan Hanoi Pedag Univ Dept Math Phuc Yen Vinh Phuc Vietnam

We prove that any iterative sequence generated by the projection decomposition algorithm of Pham Dinh et al. (Optim Methods Softw 23:609-629, 2008) in quadratic programming is bounded, provided that the quadratic prog... 详细信息

关键词： Quadratic programming dc algorithm dcA sequence Convergence Boundedness

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A New Approach for Optimizing Traffic Signals in Networks Considering Rerouting 3rd

A New Approach for Optimizing Traffic Signals in Networks Co...

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3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO)

作者： Duc Quynh Tran Ba Thang Phan Nguyen Quang Thuan Nguyen Vietnam Natl Univ Agr FITA Hanoi Vietnam Hanoi Univ Sci & Technol SAMI Hanoi Vietnam

ISBN: (纸本)9783319181615;9783319181608

In traffic signal control, the determination of the green time and the cycle time for optimizing the total delay time is an important problem. We investigate the problem by considering the change of the associated flows at User Equilibrium resulting from the given signal timings (rerouting). Existing models are solved by the heuristic-based solution methods that require commercial simulation softwares. In this work, we build two new formulations for the problem above and propose two methods to directly solve them. These are based on genetic algorithms (GA) and difference of convex functions algorithms (dcA).

关键词： dc algorithm Genetic algorithm Traffic signal control Bi-level optimization model

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Solving Relaxation Orienteering Problem Using dcA-CUT 3rd

Solving Relaxation Orienteering Problem Using DCA-CUT

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3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO)

作者： Anh Son Ta Hoai An Le Thi Trong Sy Ha Hanoi Univ Sicence & Technol SAMI Hanoi Vietnam Lorraine Univ LITA Metz France

ISBN: (纸本)9783319181615;9783319181608

Orienteering problem is well-known as a NP-hard problem in transportation with many applications. This problem aims to find a path between a given set of control points, where the source and destination points are specified with respect to maximize the total score of collected points and satisfy the distance constraint. In this paper, we first analyze the structure of a generalized orienting problem and a new solution method, based on dc programming, dcA and Cutting plane method, is introduced. Preliminary numerical experiments are reported to show the efficiency of the proposed algorithm.

关键词： Orienteering problem dc programming dc algorithm Binary Linear Integer Program

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Globally convergent dc trust-region methods

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JOURNAL OF GLOBAL OPTIMIZATION 2014年第2-3期59卷 209-225页

作者： Hoai An Le Thi Van Ngai Huynh Tao Pham Dinh Vaz, A. Ismael F. Vicente, L. N. Univ Lorraine UFR MIM LITA F-57045 Metz 01 France Univ Quynhon Dept Math Quy Nhon Vietnam Natl Inst Appl Sci Rouen Math Lab Rouen France Univ Minho Dept Prod & Syst P-4710057 Braga Portugal Univ Coimbra Dept Math CMUC P-3001501 Coimbra Portugal

In this paper, we investigate the use of dc (Difference of Convex functions) models and algorithms in the application of trust-region methods to the solution of a class of nonlinear optimization problems where the constrained set is closed and convex (and, from a practical point of view, where projecting onto the feasible region is computationally affordable). We consider dc local models for the quadratic model of the objective function used to compute the trust-region step, and apply a primal-dual subgradient method to the solution of the corresponding trust-region subproblems. One is able to prove that the resulting scheme is globally convergent to first-order stationary points. The theory requires the use of exact second-order derivatives but, in turn, the computation of the trust-region step asks only for one projection onto the feasible region (in comparison to the calculation of the generalized Cauchy point which may require more). The numerical efficiency and robustness of the proposed new scheme when applied to bound-constrained problems is measured by comparing its performance against some of the current state-of-the-art nonlinear programming solvers on a vast collection of test problems.

关键词： Trust-region methods dc algorithm Global convergence Bound constraints

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Properties of two dc algorithms in quadratic programming

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JOURNAL OF GLOBAL OPTIMIZATION 2011年第3期49卷 481-495页

作者： Hoai An Le Thi Tao Pham Dinh Nguyen Dong Yen Paul Verlaine Univ Metz Ile Saulcy Lab Theoret & Appl Comp Sci LITA F-57045 Metz France Natl Inst Appl Sci INSA Rouen Lab Modelling Optimizat & Operat Res LMI F-76801 St Etienne France Vietnamese Acad Sci & Technol Inst Math Hanoi 10307 Vietnam

Some new properties of the Projection dc decomposition algorithm (we call it algorithm A) and the Proximal dc decomposition algorithm (we call it algorithm B) Pham Dinh et al. in Optim Methods Softw, 23(4): 609-629 (2008) for solving the indefinite quadratic programming problem under linear constraints are proved in this paper. Among other things, we show that dcA sequences generated by algorithm A converge to a locally unique solution if the initial points are taken from a neighborhood of it, and dcA sequences generated by either algorithm A or algorithm B are all bounded if a condition guaranteeing the solution existence of the given problem is satisfied.

关键词： Quadratic programming dc algorithm KKT point Local solution dcA sequence Convergence Boundedness

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Behavior of dcA sequences for solving the trust-region subproblem

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JOURNAL OF GLOBAL OPTIMIZATION 2012年第2期53卷 317-329页

作者： Hoai An Le Thi Tao Pham Dinh Nguyen Dong Yen Paul Verlaine Univ Metz Lab Theoret & Appl Comp Sci LITA F-57045 Metz France Natl Inst Appl Sci INSA Rouen Lab Modelling Optimizat & Operat Res LMI F-76801 St Etienne France Vietnamese Acad Sci & Technol Inst Math Hanoi 10307 Vietnam

From our results it follows that any dcA sequence for solving the trust-region subproblem (see Pham Dinh and Le Thi, in SIAM J Optim 8:476-505, 1998) is convergent provided that the basic matrix of the problem is nonsingular and it does not have multiple negative eigenvalues. Besides, under this additional assumption, there exists such an open set containing the global minimizers and the unique local-nonglobal minimizer (if such exists) that any dcA sequence with the initial point from is contained in the set and converges to a global minimizer or the local-nonglobal minimizer. Various examples are given to illustrate the limiting behavior and stability of the dcA sequences. Structure of the KKT point set of the trust-region subproblem is also analyzed.

关键词： Trust-region subproblem dc algorithm dcA sequence Limiting behavior and stability Multiplicity of nonpositive eigenvalue

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