26 results
Search Results
2. Weak and strong convergences of the generalized penalty Forward-Forward and Forward-Backward splitting algorithms for solving bilevel hierarchical pseudomonotone equilibrium problems.
- Author
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Riahi, Hassan, Chbani, Zaki, and Loumi, Moulay-Tayeb
- Subjects
STOCHASTIC convergence ,NUMERICAL analysis ,MATHEMATICAL optimization ,MATHEMATICAL analysis ,BANACH spaces - Abstract
In this paper, we present two penalty-splitting inspired iteration schemes (PFFSA) and (PFFSA) for hierarchical equilibrium problems in Hilbert space. Based on the Opial-Passty lemma, we propose weak ergodic convergence and weak convergence of the iterative sequences generated by the Forward-Forward algorithm (PFFSA) and the Forward-Backward algorithm (PFFSA), which are proved under quite mild conditions: the bifunction of the two level equilibrium problems are supposed pseudomonotone. For strong convergence, we first add a strong monotonicity condition on the objective bifunction. We present after, a strong convergence result of algorithm (PFFSA) by adding a topological assumption, i.e. the objective bifunction is of class . Some examples are given to illustrate our results. The first example deals with pseudomonotone variational inequalities and convex minimization problem in the upper level problem. In the second one, we propose a convex minimization in the lower-level problem, where strong convergence of (PFFSA) to a minimum point is insured under infcompactness condition for objective function. These convergence results are new and generalize some recent results in this field. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
3. PARTIAL ERROR BOUND CONDITIONS AND THE LINEAR CONVERGENCE RATE OF THE ALTERNATING DIRECTION METHOD OF MULTIPLIERS.
- Author
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YONGCHAO LIU, XIAOMING YUAN, SHANGZHI ZENG, and JIN ZHANG
- Subjects
STOCHASTIC convergence ,NUMERICAL analysis ,MATHEMATICAL analysis ,DIFFERENTIAL equations ,MATHEMATICAL optimization - Abstract
In the literature, error bound conditions have been widely used to study the linear convergence rates of various first-order algorithms. Most of the literature focuses on how to ensure these error bound conditions, usually posing numerous assumptions or special structures on the model under discussion. In this paper, we focus on the alternating direction method of multipliers (ADMM) and show that the known error bound conditions for studying the ADMM's linear convergence rate can indeed be further weakened if the error bound is studied over the specific iterative sequence it generates. An error bound condition based on ADMM's iterations is thus proposed, and linear convergence under this condition is proved. Furthermore, taking advantage of a specific feature of ADMM's iterative scheme by which part of the perturbation is automatically zero, we propose the so-called partial error bound condition, which is weaker than known error bound conditions in the literature, and we derive the linear convergence rate of ADMM. We further show that this partial error bound condition is useful for interpreting the difference if the two primal variables are updated in different orders when implementing the ADMM. This has been empirically observed in the literature, yet no theory is known. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
4. Trust region methods for solving multiobjective optimisation.
- Author
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Qu, Shaojian, Goh, Mark, and Liang, Bing
- Subjects
PROBLEM solving ,MATHEMATICAL optimization ,ALGORITHMS ,STOCHASTIC convergence ,NONSMOOTH optimization ,MATHEMATICAL analysis ,NUMERICAL analysis - Abstract
This paper first proposes a trust region algorithm to obtain a stationary point of unconstrained multiobjective optimisation problem. Under suitable assumptions, the global convergence of the new algorithm is established. We then extend the trust region method to solve the non-smooth multiobjective optimisation problem. [ABSTRACT FROM PUBLISHER]
- Published
- 2013
- Full Text
- View/download PDF
5. A new trust region method with adaptive radius for unconstrained optimization.
- Author
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Cui, Zhaocheng and Wu, Boying
- Subjects
MATHEMATICAL optimization ,STOCHASTIC convergence ,ITERATIVE methods (Mathematics) ,GLOBAL analysis (Mathematics) ,PROBLEM solving ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
In this paper, we propose a new adaptive trust region method for unconstrained optimization problems. In the new method, we use the previous and the current iterative information and a new update rule to define the trust region radius at each iterate. The global and superlinear convergence properties of the method are established under reasonable assumptions. Preliminary numerical results show that the new method is efficient and attractive for unconstrained optimization problems. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
6. A Class of Augmented Filled Functions.
- Author
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Xian Liu
- Subjects
NONLINEAR programming ,MATHEMATICAL programming ,MATHEMATICAL analysis ,MATHEMATICAL optimization ,COMBINATORICS ,ALGORITHMS ,NUMERICAL analysis ,NUMERICAL calculations ,STOCHASTIC convergence - Abstract
The filled function method is an effective approach to find the global minimizer. Two of the recently proposed filled functions are H(X) and L
2 (X). Although their numerical behavior is acceptable, they are not defined everywhere. This paper proposes a class of augmented filled functions with improved analyticity. Issues covered in the presented work include: theoretical properties, convergence analysis, geometric interpretation, algorithms, and numerical experiments. The overall performance of the new approach is comparable to the recently proposed ones. [ABSTRACT FROM AUTHOR]- Published
- 2006
- Full Text
- View/download PDF
7. Efficient random coordinate descent algorithms for large-scale structured nonconvex optimization.
- Author
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Patrascu, Andrei and Necoara, Ion
- Subjects
STOCHASTIC convergence ,GLOBAL optimization ,MATHEMATICAL optimization ,ALGORITHMS ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function consisting of a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known. Further, we consider both cases: unconstrained and linearly constrained nonconvex problems. For optimization problems of the above structure, we propose random coordinate descent algorithms and analyze their convergence properties. For the general case, when the objective function is nonconvex and composite we prove asymptotic convergence for the sequences generated by our algorithms to stationary points and sublinear rate of convergence in expectation for some optimality measure. Additionally, if the objective function satisfies an error bound condition we derive a local linear rate of convergence for the expected values of the objective function. We also present extensive numerical experiments for evaluating the performance of our algorithms in comparison with state-of-the-art methods. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
8. A BFGS trust-region method for nonlinear equations.
- Author
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Yuan, Gonglin, Wei, Zengxin, and Lu, Xiwen
- Subjects
MATHEMATICAL optimization ,NONLINEAR statistical models ,STOCHASTIC convergence ,QUADRATIC programming ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
In this paper, a new trust-region subproblem combining with the BFGS update is proposed for solving nonlinear equations, where the trust region radius is defined by a new way. The global convergence without the nondegeneracy assumption and the quadratic convergence are obtained under suitable conditions. Numerical results show that this method is more effective than the norm method. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
9. CONVERGENCE RATES OF THE FRONT TRACKING METHOD FOR CONSERVATION LAWS IN THE WASSERSTEIN DISTANCES.
- Author
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SOLEM, SUSANNE
- Subjects
NUMERICAL analysis ,MATHEMATICAL analysis ,STOCHASTIC convergence ,MATHEMATICAL optimization ,MATHEMATICAL models - Abstract
We prove that front tracking approximations to scalar conservation laws with convex fluxes converge at a rate of Δ x2 in the 1-Wasserstein distance W1. Assuming positive initial data, we also show that the approximations converge at a rate of Δ x in the ∞ -Wasserstein distance W∞ . Moreover, from a simple interpolation inequality between W1 and W∞ we obtain convergence rates in all the p-Wasserstein distances: Δ x
1+1/p , p ϵ [1,∞ ]. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
10. The Global Convergence of a New Mixed Conjugate Gradient Method for Unconstrained Optimization.
- Author
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Yang Yueting and Cao Mingyuan
- Subjects
STOCHASTIC convergence ,CONJUGATE gradient methods ,MATHEMATICAL optimization ,NONLINEAR theories ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
We propose and generalize a new nonlinear conjugate gradient method for unconstrained optimization. The global convergence is proved with the Wolfe line search. Numerical experiments are reported which support the theoretical analyses and show the presented methods outperforming CGDESCENT method. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
11. A sharp cut algorithm for optimization
- Author
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Inamdar, S.R., Karimi, I.A., Parulekar, S.J., and Kulkarni, B.D.
- Subjects
- *
COMPUTER algorithms , *MATHEMATICAL optimization , *LINEAR programming , *STOCHASTIC convergence , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we introduce a new cutting plane algorithm which is computationally less expensive and more efficient than Kelley’s algorithm. This new cutting plane algorithm uses an intersection cut of three types of cutting planes. We find from numerical results that the global search method formed using successive linear programming and a new intersection set is at least twice as fast as Kelley’s cutting planes. The necessary mathematical analysis and convergence theorem are provided. The key findings are illustrated via optimization of a cascade of three CSTRs. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
12. Modified self-adaptive projection method for solving pseudomonotone variational inequalities
- Author
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Yu, Zeng, Shao, Hu, and Wang, Guodong
- Subjects
- *
VARIATIONAL inequalities (Mathematics) , *MATHEMATICAL optimization , *STOCHASTIC convergence , *MATHEMATICAL analysis , *NUMERICAL analysis , *CALCULUS of variations - Abstract
Abstract: In this paper, a self-adaptive projection method with a new search direction for solving pseudomonotone variational inequality (VI) problems is proposed, which can be viewed as an extension of the methods in [B.S. He, X.M. Yuan, J.Z. Zhang, Comparison of two kinds of prediction-correction methods for monotone variational inequalities, Computational Optimization and Applications 27 (2004) 247–267] and [X.H. Yan, D.R. Han, W.Y. Sun, A self-adaptive projection method with improved step-size for solving variational inequalities, Computers & Mathematics with Applications 55 (2008) 819–832]. The descent property of the new search direction is proved, which is useful to guarantee the convergence. Under the relatively relaxed condition that F is continuous and pseudomonotone, the global convergence of the proposed method is proved. Numerical experiments are provided to illustrate the efficiency of the proposed method. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
13. Optimized Schwarz coupling of Bidomain and Monodomain models in electrocardiology.
- Author
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Gerardo-Giorda, Luca, Perego, Mauro, and Veneziani, Alessandro
- Subjects
- *
MATHEMATICAL optimization , *SCHWARTZ distributions , *ELECTROCARDIOGRAPHY , *MATHEMATICAL analysis , *STOCHASTIC convergence , *NUMERICAL analysis - Abstract
The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart. However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features of this system. For this reason, a simplification of this model, called Monodomain problem is quite often adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in the presence of applied currents and in the regions where the upstroke or the late recovery of the action potential is occurring. In this paper we investigate a domain decomposition approach for this problem, where the entire computational domain is suitably split and the two models are solved in different subdomains. Since the mathematical features of the two problems are rather different, the heterogeneous coupling is non trivial. Here we investigate appropriate interface matching conditions for the coupling on non overlapping domains. Moreover, we pursue an Optimized Schwarz approach for the numerical solution of the heterogeneous problem. Convergence of the iterative method is analyzed by means of a Fourier analysis. We investigate the parameters to be selected in the matching radiation-type conditions to accelerate the convergence. Numerical results both in two and three dimensions illustrate the effectiveness of the coupling strategy. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
14. A semismooth Newton method for topology optimization
- Author
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Amstutz, Samuel
- Subjects
- *
SMOOTHNESS of functions , *NEWTON-Raphson method , *MATHEMATICAL optimization , *STOCHASTIC convergence , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: This paper deals with elliptic optimal control problems for which the control function is constrained to assume values in {0, 1}. Based on an appropriate formulation of the optimality system, a semismooth Newton method is proposed for the solution. Convergence results are proved, and some numerical tests illustrate the efficiency of the method. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
15. A New Method for Solving Unconstrained Optimization Problems.
- Author
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Liliu Mo and Ling Hong
- Subjects
MATHEMATICAL optimization ,MATHEMATICS ,MATHEMATICAL analysis ,NUMERICAL analysis ,STOCHASTIC convergence ,EQUATIONS - Abstract
In this paper, a new conjugate gradient formula β
New k is given to compute the search directions for unconstrained optimization problems. General convergence results for the proposed formula with some line searches such as the exact line search, the Grippo-Lucidi line search and the Wolfe-Powell line search are discussed. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. The given formula βNew k ⩾ 0, and the search directions dk which are generated by the given βNew k under the strong Wolfe-Powell line search satisfy the sufficient descent condition. Preliminary numerical results show that the proposed methods are efficient. [ABSTRACT FROM AUTHOR]- Published
- 2009
16. A new Liu–Storey type nonlinear conjugate gradient method for unconstrained optimization problems
- Author
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Zhang, Li
- Subjects
- *
CONJUGATE gradient methods , *STOCHASTIC convergence , *MATHEMATICAL optimization , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: Although the Liu–Storey (LS) nonlinear conjugate gradient method has a similar structure as the well-known Polak–Ribière–Polyak (PRP) and Hestenes–Stiefel (HS) methods, research about this method is very rare. In this paper, based on the memoryless BFGS quasi-Newton method, we propose a new LS type method, which converges globally for general functions with the Grippo–Lucidi line search. Moreover, we modify this new LS method such that the modified scheme is globally convergent for nonconvex minimization if the strong Wolfe line search is used. Numerical results are also reported. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
17. An affine scaling optimal path method with interior backtracking curvilinear technique for linear constrained optimization
- Author
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Wang, Yunjuan and Zhu, Detong
- Subjects
- *
MATHEMATICAL optimization , *PATHS & cycles in graph theory , *ALGORITHMS , *STOCHASTIC convergence , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Abstract: This paper presents an affine scaling optimal path approach in association with nonmonotonic interior backtracking line search technique for nonlinear optimization subject to linear constraints. We shall employ the eigensystem decomposition and affine scaling mapping to form affine scaling optimal curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis is given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
18. A limited memory BFGS-type method for large-scale unconstrained optimization
- Author
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Xiao, Yunhai, Wei, Zengxin, and Wang, Zhiguo
- Subjects
- *
MATHEMATICAL optimization , *MATHEMATICAL analysis , *NUMERICAL analysis , *MAGNETIC memory (Computers) , *STOCHASTIC convergence - Abstract
Abstract: In this paper, a new numerical method for solving large-scale unconstrained optimization problems is presented. It is derived from a modified BFGS-type update formula by Wei, Li, and Qi. It is observed that the update formula can be extended to the framework of limited memory scheme with hardly more storage or arithmetic operations. Under some suitable conditions, the global convergence property is established. The implementations of the method on a set of CUTE problems indicate that this extension is beneficial to the performance of the algorithm. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
19. A TRUST-REGION ALGORITHM FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION[sup*1].
- Author
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Xiaojiao Tong and Shuzi Zhou
- Subjects
- *
ALGORITHMS , *STOCHASTIC convergence , *MATHEMATICAL optimization , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
This paper presents a new trust-region algorithm for n-dimension nonlinear optimization subject to m nonlinear inequality constraints. Equivalent KKT conditions are derived, which is the basis for constructing the new algorithm. Global convergence of the algorithm to a first-order KKT point is established under mild conditions on the trial steps, local quadratic convergence theorem is proved for nondegenerate minimizer point. Numerical experiment is presented to show the effectiveness of our approach. [ABSTRACT FROM AUTHOR]
- Published
- 2003
20. Parameter estimation of shallow wave equation via cuckoo search.
- Author
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Zhang, Xin-Ming
- Subjects
MATHEMATICAL optimization ,NUMERICAL analysis ,PARAMETER estimation ,ESTIMATION theory ,MATHEMATICAL models ,APPROXIMATION theory ,STOCHASTIC convergence ,MATHEMATICAL analysis - Abstract
In this study, cuckoo search is introduced for performing the parameter estimation of shallow wave equation for the first time. Cuckoo search (CS) is invented based on the inspiration of brood parasitic behavior of some cuckoo species in combination with the Lévy flight behavior. These meta-heuristics have been successfully used for solving some optimization problems with promising results. However, this emerging optimization method has not been applied in parameter inversion problem. This study reports a CS-based parameter estimation method to inverse the roughness coefficient and the coefficient of eddy viscosity under some specific conditions. Simulation results and experimental data show that cuckoo search offers a reliable performance for these parameter estimation problems. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
21. NONSMOOTH ALGORITHMS AND NESTEROV'S SMOOTHING TECHNIQUE FOR GENERALIZED FERMAT-TORRICELLI PROBLEMS.
- Author
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NGUYEN MAU NAM, NGUYEN THAI AN, RECTOR, R. BLAKE, and JIE SUN
- Subjects
NUMERICAL analysis ,MATHEMATICAL analysis ,SMOOTHING (Numerical analysis) ,SUBGRADIENT methods ,MATHEMATICAL optimization ,STOCHASTIC convergence - Abstract
We present algorithms for solving a number of new models of facility location which generalize the classical Fermat-Torricelli problem. Our first approach involves using Nesterov's smoothing technique and the minimization majorization principle to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the nondifferentiability of the cost functions. Convergence results of the algorithms are proved and numerical tests are presented to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
22. The semi-smooth Newton method for variationally discretized control constrained elliptic optimal control problems; implementation, convergence and globalization.
- Author
-
Hinze, Michael and Vierling, Morten
- Subjects
NEWTON-Raphson method ,CONTROL theory (Engineering) ,STOCHASTIC convergence ,NUMERICAL analysis ,MATHEMATICAL optimization ,MATHEMATICAL analysis ,ERROR analysis in mathematics ,MATHEMATICAL proofs - Abstract
Combining the numerical concept of variational discretization and semi-smooth Newton methods for the numerical solution of pde-constrained optimization with control constraints, we place special emphasis on the implementation and globalization of the numerical algorithm. We prove fast local convergence of a globalized algorithm and illustrate our analytical and algorithmical findings by numerical experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
23. A recursive ℓ∞-trust-region method for bound-constrained nonlinear optimization.
- Author
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Gratton, Serge, Mouffe, Mélodie, Toint, Philippe L., and Weber-Mendonça, Melissa
- Subjects
MATHEMATICAL optimization ,STOCHASTIC convergence ,NUMERICAL analysis ,MATHEMATICAL analysis ,MULTIGRID methods (Numerical analysis) - Abstract
A recursive trust-region method is introduced for the solution of bound-cons-trained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the trust region, which is well adapted to the handling of bounds and also to the use of successive coordinate minimization as a smoothing technique. Numerical tests motivate a theoretical analysis showing convergence to first-order critical points irrespective of the starting point. [ABSTRACT FROM PUBLISHER]
- Published
- 2008
- Full Text
- View/download PDF
24. A NEW ACTIVE SET ALGORITHM FOR BOX CONSTRAINED OPTIMIZATION.
- Author
-
Hager, William W. and Hongchao Zhang
- Subjects
ALGORITHMS ,MATHEMATICAL optimization ,STOCHASTIC convergence ,NUMERICAL analysis ,MATHEMATICAL analysis - Abstract
An active set algorithm (ASA) for box constrained optimization is developed. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for branching between the two steps. Global convergence to a stationary point is established. For a nondegenerate stationary point, the algorithm eventually reduces to unconstrained optimization without restarts. Similarly, for a degenerate stationary point, where the strong second order sufficient optimality condition holds, the algorithm eventually reduces to unconstrained optimization without restarts. A specific implementation of the ASA is given which exploits the recently developed cyclic Barzilai-Borwein (CBB) algorithm for the gradient projection step and the recently developed conjugate gradient algorithm CG_DESCENT for unconstrained optimization. Numerical experiments are presented using box constrained problems in the CUTEr and MINPACK-2 test problem libraries. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
25. The cyclic Barzilai-–Borwein method for unconstrained optimization.
- Author
-
Yu-Hong Dai, Hager, William W., Schittkowski, Klaus, and Hongchao Zhang
- Subjects
MATHEMATICAL optimization ,MATHEMATICAL analysis ,STOCHASTIC convergence ,CONJUGATE gradient methods ,NUMERICAL analysis - Abstract
In the cyclic Barzilai–Borwein (CBB) method, the same Barzilai–Borwein (BB) stepsize is reused for m consecutive iterations. It is proved that CBB is locally linearly convergent at a local minimizer with positive definite Hessian. Numerical evidence indicates that when m > n/2 ≥ 3, where n is the problem dimension, CBB is locally superlinearly convergent. In the special case m = 3 and n = 2, it is proved that the convergence rate is no better than linear, in general. An implementation of the CBB method, called adaptive cyclic Barzilai–Borwein (ACBB), combines a non-monotone line search and an adaptive choice for the cycle length m. In numerical experiments using the CUTEr test problem library, ACBB performs better than the existing BB gradient algorithm, while it is competitive with the well-known PRP+ conjugate gradient algorithm. [ABSTRACT FROM PUBLISHER]
- Published
- 2006
- Full Text
- View/download PDF
26. LINE SEARCH TECHNIQUES BASED ON INTERPOLATING POLYNOMIALS USING FUNCTION VALUES ONLY.
- Author
-
Tamir, Arie
- Subjects
INTERPOLATION ,NUMERICAL analysis ,POLYNOMIALS ,STOCHASTIC convergence ,GOLDEN ratio ,ALGORITHMS ,MATHEMATICAL analysis ,MATHEMATICAL optimization ,INDUSTRIAL efficiency - Abstract
In this study we derive the order of convergence of some line search techniques based on fitting polynomials, using function values only. It is shown that the order of convergence increases with the degree of the polynomial. If viewed as a sequence, the orders approach the Golden Section Ratio when the degree of the polynomial tends to infinity. [ABSTRACT FROM AUTHOR]
- Published
- 1976
- Full Text
- View/download PDF
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