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1.
Lingchen Kong Levent Tunçel Naihua Xiu 《Journal of Optimization Theory and Applications》2011,148(2):364-389
In this paper we consider the linear symmetric cone programming (SCP). At a Karush-Kuhn-Tucker (KKT) point of SCP, we present
the important conditions equivalent to the nonsingularity of Clarke’s generalized Jacobian of the KKT nonsmooth system, such
as primal and dual constraint nondegeneracy, the strong regularity, and the nonsingularity of the B-subdifferential of the
KKT system. This affirmatively answers an open question by Chan and Sun (SIAM J. Optim. 19:370–396, 2008). 相似文献
2.
Kaori Sugiki Yasushi Narushima Hiroshi Yabe 《Journal of Optimization Theory and Applications》2012,153(3):733-757
In this paper, we propose a three-term conjugate gradient method based on secant conditions for unconstrained optimization
problems. Specifically, we apply the idea of Dai and Liao (in Appl. Math. Optim. 43: 87–101, 2001) to the three-term conjugate gradient method proposed by Narushima et al. (in SIAM J. Optim. 21: 212–230, 2011). Moreover, we derive a special-purpose three-term conjugate gradient method for a problem, whose objective function has
a special structure, and apply it to nonlinear least squares problems. We prove the global convergence properties of the proposed
methods. Finally, some numerical results are given to show the performance of our methods. 相似文献
3.
Vladimir Shikhman 《Journal of Global Optimization》2008,42(4):619-623
We consider the interesting smoothing method of global optimization recently proposed in Lau and Kwong (J Glob Optim 34:369–398,
2006) . In this method smoothed functions are solutions of an initial-value problem for a heat diffusion equation with external
heat source. As shown in Lau and Kwong (J Glob Optim 34:369–398, 2006), the source helps to control global minima of the smoothed
functions—they are not shifted during the smoothing. In this note we point out that for certain (families of) objective functions
the proposed method unfortunately does not affect the functions, in the sense, that the smoothed functions coincide with the
respective objective function. The key point here is that the Laplacian might be too weak in order to smooth out critical
points. 相似文献
4.
John A. Ford Yasushi Narushima Hiroshi Yabe 《Computational Optimization and Applications》2008,40(2):191-216
Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of
matrices. Recently, seeking fast convergence of these methods, Dai and Liao (Appl. Math. Optim. 43:87–101, 2001) proposed a conjugate gradient method based on the secant condition of quasi-Newton methods, and later Yabe and Takano (Comput.
Optim. Appl. 28:203–225, 2004) proposed another conjugate gradient method based on the modified secant condition. In this paper, we make use of a multi-step
secant condition given by Ford and Moghrabi (Optim. Methods Softw. 2:357–370, 1993; J. Comput. Appl. Math. 50:305–323, 1994) and propose two new conjugate gradient methods based on this condition. The methods are shown to be globally convergent
under certain assumptions. Numerical results are reported. 相似文献
5.
We consider a class of unconstrained nonsmooth convex optimization problems, in which the objective function is the sum of
a convex smooth function on an open subset of matrices and a separable convex function on a set of matrices. This problem
includes the covariance selection problem that can be expressed as an ℓ
1-penalized maximum likelihood estimation problem. In this paper, we propose a block coordinate gradient descent method (abbreviated
as BCGD) for solving this class of nonsmooth separable problems with the coordinate block chosen by a Gauss-Seidel rule. The
method is simple, highly parallelizable, and suited for large-scale problems. We establish global convergence and, under a
local Lipschizian error bound assumption, linear rate of convergence for this method. For the covariance selection problem,
the method can terminate in O(n3/e){O(n^3/\epsilon)} iterations with an e{\epsilon}-optimal solution. We compare the performance of the BCGD method with the first-order methods proposed by Lu (SIAM J Optim
19:1807–1827, 2009; SIAM J Matrix Anal Appl 31:2000–2016, 2010) for solving the covariance selection problem on randomly generated instances. Our numerical experience suggests that the
BCGD method can be efficient for large-scale covariance selection problems with constraints. 相似文献
6.
In this paper, we analyze the outer approximation property of the algorithm for generalized semi-infinite programming from
Stein and Still (SIAM J. Control Optim. 42:769–788, 2003). A simple bound on the regularization error is found and used to formulate a feasible numerical method for generalized semi-infinite programming with convex lower-level problems. That is, all iterates of the
numerical method are feasible points of the original optimization problem. The new method has the same computational cost
as the original algorithm from Stein and Still (SIAM J. Control Optim. 42:769–788, 2003). We also discuss the merits of this approach for the adaptive convexification algorithm, a feasible point method for standard
semi-infinite programming from Floudas and Stein (SIAM J. Optim. 18:1187–1208, 2007). 相似文献
7.
Napsu Karmitsa Mario Tanaka Filho José Herskovits 《Journal of Optimization Theory and Applications》2011,148(3):528-549
Nowadays, solving nonsmooth (not necessarily differentiable) optimization problems plays a very important role in many areas
of industrial applications. Most of the algorithms developed so far deal only with nonsmooth convex functions. In this paper,
we propose a new algorithm for solving nonsmooth optimization problems that are not assumed to be convex. The algorithm combines
the traditional cutting plane method with some features of bundle methods, and the search direction calculation of feasible
direction interior point algorithm (Herskovits, J. Optim. Theory Appl. 99(1):121–146, 1998). The algorithm to be presented generates a sequence of interior points to the epigraph of the objective function. The accumulation
points of this sequence are solutions to the original problem. We prove the global convergence of the method for locally Lipschitz
continuous functions and give some preliminary results from numerical experiments. 相似文献
8.
In this paper, a priori error estimates for space–time finite element discretizations of optimal control problems governed
by semilinear parabolic PDEs and subject to pointwise control constraints are derived. We extend the approach from Meidner
and Vexler (SIAM Control Optim
47(3):1150–1177, 2008; SIAM Control Optim 47(3):1301–1329, 2008) where linear-quadratic problems have been considered, discretizing the state equation by usual conforming finite elements
in space and a discontinuous Galerkin method in time. Error estimates for controls discretized by piecewise constant functions
in time and cellwise constant functions in space are derived in detail and we explain how error estimate for further discretization
approaches, e.g., cellwise linear discretization in space, the postprocessing approach from Meyer and R?sch (SIAM J Control
Optim 43:970–985, 2004), and the variationally discrete approach from Hinze (J Comput Optim Appl 30:45–63, 2005) can be obtained. In addition, we derive an estimate for a setting with finitely many time-dependent controls. 相似文献
9.
In this note we correct and improve a zero duality gap result in extended monotropic programming given by Bertsekas (J. Optim.
Theory Appl. 139:209–225, 2008). 相似文献
10.
《Set-Valued Analysis》2008,16(2-3):129-155
We give implicit multifunction results generalizing to multifunctions the Robinson’s implicit function theorem (Robinson,
Math Oper Res 16(2):292–309, 1991). To this end, we use parametric error bounds estimates for a suitable function refining the one given in Azé and Corvellec
(ESAIM Control Optim Calc Var 10:409–425, 2004). Sharp approximations of the implicit multifunctions are given extending the results of Nachi and Penot (Control Cybernet
35:871–901, 2005).
Dedicated to Boris Mordukhovich in honour of his 60th birthday. 相似文献
11.
In this paper, we consider a one-dimensional dam-river system studied by Chentouf and Wang (SIAM J. Control Optim. 47: 2275–2302,
2008). Then, using the frequency multiplier method, we provide a simple and alternative proof of stabilization and regulation
results obtained in the work cited above. Moreover, we relax the conditions on the feedback gains involved in the feedback
law and give a partial answer to the open problem left by the authors Chentouf and Wang (J. Optim. Theory Appl. 134: 223–239,
2007 and SIAM J. Control Optim. 47: 2275–2302, 2008) concerning the tuning of the gains. 相似文献
12.
We extend some results due to Thanh-Hao (Acta Math. Vietnam. 31: 283–289, [2006]) and Noor (J. Optim. Theory Appl. 115:447–452, [2002]). The first paper established a convergence theorem for the Tikhonov regularization method (TRM) applied to finite-dimensional
pseudomonotone variational inequalities (VIs), answering in the affirmative an open question stated by Facchinei and Pang
(Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer, New York, [2003]). The second paper discussed the application of the proximal point algorithm (PPA) to pseudomonotone VIs. In this paper,
new facts on the convergence of TRM and PPA (both the exact and inexact versions of PPA) for pseudomonotone VIs in Hilbert
spaces are obtained and a partial answer to a question stated in (Acta Math. Vietnam. 31:283–289, [2006]) is given. As a byproduct, we show that the convergence theorem for inexact PPA applied to infinite-dimensional monotone
variational inequalities can be proved without using the theory of maximal monotone operators.
This research was supported in part by a grant from the National Sun Yat-Sen University, Kaohsiung, Taiwan. It has been carried
out under the agreement between the National Sun Yat-Sen University, Kaohsiung, Taiwan and the University of Pisa, Pisa, Italy.
The authors thank the anonymous referee for useful comments and suggestions. 相似文献
13.
In this paper, we propose a new smoothing Broyden-like method for solving nonlinear complementarity problem with P
0 function. The presented algorithm is based on the smoothing symmetrically perturbed minimum function φ(a, b) = min{a, b} and makes use of the derivative-free line search rule of Li et al. (J Optim Theory Appl 109(1):123–167, 2001). Without requiring any strict complementarity assumption at the P
0-NCP solution, we show that the iteration sequence generated by the suggested algorithm converges globally and superlinearly
under suitable conditions. Furthermore, the algorithm has local quadratic convergence under mild assumptions. Some numerical
results are also reported in this paper. 相似文献
14.
In this paper we investigate POD discretizations of abstract linear–quadratic optimal control problems with control constraints.
We apply the discrete technique developed by Hinze (Comput. Optim. Appl. 30:45–61, 2005) and prove error estimates for the corresponding discrete controls, where we combine error estimates for the state and the
adjoint system from Kunisch and Volkwein (Numer. Math. 90:117–148, 2001; SIAM J. Numer. Anal. 40:492–515, 2002). Finally, we present numerical examples that illustrate the theoretical results. 相似文献
15.
When applied to large-scale separable optimization problems, the recently developed surrogate subgradient method for Lagrangian
relaxation (Zhao et al.: J. Optim. Theory Appl. 100, 699–712, 1999) does not need to solve optimally all the subproblems to update the multipliers, as the traditional subgradient method requires.
Based on it, the penalty surrogate subgradient algorithm was further developed to address the homogenous solution issue (Guan
et al.: J. Optim. Theory Appl. 113, 65–82, 2002; Zhai et al.: IEEE Trans. Power Syst. 17, 1250–1257, 2002). There were flaws in the proofs of Zhao et al., Guan et al., and Zhai et al.: for problems with inequality constraints,
projection is necessary to keep the multipliers nonnegative; however, the effects of projection were not properly considered.
This note corrects the flaw, completes the proofs, and asserts the correctness of the methods.
This work is supported by the NSFC Grant Nos. 60274011, 60574067, the NCET program (No. NCET-04-0094) of China. The third
author was supported in part by US National Science Foundation under Grants ECS-0323685 and DMI-0423607. 相似文献
16.
E. A. Al-Said A. H. Almualim M. A. Noor 《Journal of Optimization Theory and Applications》2010,146(3):810-812
In this article some comments on the paper “parametric cubic spline approach to the solution of a system of second order boundary
value problems” in (Khan and Aziz, J. Optim. Theory Appl. 118:45–54, 2003) are given. This paper concerns with a numerical method for solving a second order boundary value problem associated with
obstacle, unilateral and contact problems. Corrections are given for the convergence analysis of the numerical method and
the computational experiments. 相似文献
17.
In this paper, we extend the auxiliary principle (Cohen in J. Optim. Theory Appl. 49:325–333, 1988) to study a class of Lions-Stampacchia variational inequalities in Hilbert spaces. Our method consists in approximating,
in the subproblems, the nonsmooth convex function by a sequence of piecewise linear and convex functions, as in the bundle
method for nonsmooth optimization. This makes the subproblems more tractable. We show the existence of a solution for this
Lions-Stampacchia variational inequality and explain how to build a new iterative scheme and a new stopping criterion. This
iterative scheme and criterion are different from those commonly used in the special case of nonsmooth optimization. We study
also the convergence of iterative sequences generated by the algorithm.
This work was supported by the National Natural Science Foundation of China (10671135), the Specialized Research Fund for
the Doctoral Program of Higher Education (20060610005), the National Natural Science Foundation of Sichuan Education Department
of China (07ZB068) and the Open Fund (PLN0703) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest
Petroleum University). 相似文献
18.
In this paper, we present a measure of distance in a second-order cone based on a class of continuously differentiable strictly
convex functions on ℝ++. Since the distance function has some favorable properties similar to those of the D-function (Censor and Zenios in J. Optim.
Theory Appl. 73:451–464 [1992]), we refer to it as a quasi D-function. Then, a proximal-like algorithm using the quasi D-function is proposed and applied
to the second-cone programming problem, which is to minimize a closed proper convex function with general second-order cone
constraints. Like the proximal point algorithm using the D-function (Censor and Zenios in J. Optim. Theory Appl. 73:451–464
[1992]; Chen and Teboulle in SIAM J. Optim. 3:538–543 [1993]), under some mild assumptions we establish the global convergence of the algorithm expressed in terms of function values;
we show that the sequence generated by the proposed algorithm is bounded and that every accumulation point is a solution to
the considered problem.
Research of Shaohua Pan was partially supported by the Doctoral Starting-up Foundation (B13B6050640) of GuangDong Province.
Jein-Shan Chen is a member of the Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s
work was partially supported by National Science Council of Taiwan. 相似文献
19.
A new iterative algorithm based on the inexact-restoration (IR) approach combined with the filter strategy to solve nonlinear
constrained optimization problems is presented. The high level algorithm is suggested by Gonzaga et al. (SIAM J. Optim. 14:646–669,
2003) but not yet implement—the internal algorithms are not proposed. The filter, a new concept introduced by Fletcher and Leyffer
(Math. Program. Ser. A 91:239–269, 2002), replaces the merit function avoiding the penalty parameter estimation and the difficulties related to the nondifferentiability.
In the IR approach two independent phases are performed in each iteration, the feasibility and the optimality phases. The
line search filter is combined with the first one phase to generate a “more feasible” point, and then it is used in the optimality
phase to reach an “optimal” point.
Numerical experiences with a collection of AMPL problems and a performance comparison with IPOPT are provided.
相似文献
20.
We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Newton-type methods,
under mild differentiability conditions. It turns out that our sufficient convergence conditions are weaker, and the error
bounds are tighter than in earlier studies in some interesting cases (Chen, Ann Inst Stat Math 42:387–401, 1990; Chen, Numer Funct Anal Optim 10:37–48, 1989; Cianciaruso, Numer Funct Anal Optim 24:713–723, 2003; Cianciaruso, Nonlinear Funct Anal Appl 2009; Dennis 1971; Deuflhard 2004; Deuflhard, SIAM J Numer Anal 16:1–10, 1979; Gutiérrez, J Comput Appl Math 79:131–145, 1997; Hernández, J Optim Theory Appl 109:631–648, 2001; Hernández, J Comput Appl Math 115:245–254, 2000; Huang, J Comput Appl Math 47:211–217, 1993; Kantorovich 1982; Miel, Numer Math 33:391–396, 1979; Miel, Math Comput 34:185–202, 1980; Moret, Computing 33:65–73, 1984; Potra, Libertas Mathematica 5:71–84, 1985; Rheinboldt, SIAM J Numer Anal 5:42–63, 1968; Yamamoto, Numer Math 51: 545–557, 1987; Zabrejko, Numer Funct Anal Optim 9:671–684, 1987; Zinc̆ko 1963). Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar-type, and a differential
equation are also provided in this study. 相似文献