共查询到20条相似文献,搜索用时 15 毫秒
1.
Deren Han 《Journal of Mathematical Analysis and Applications》2007,336(1):727-737
One of the popular solution methods for the complementarity problem over symmetric cones is to reformulate it as the global minimization of a certain merit function. An important question to be answered for this class of methods is under what conditions the level sets of the merit function are bounded (the coerciveness of the merit function). In this paper, we introduce the generalized weak-coerciveness of a continuous transformation. Under this condition, we prove the coerciveness of some merit functions, such as the natural residual function, the normal map, and the Fukushima-Yamashita function for complementarity problems over symmetric cones. We note that this is a much milder condition than strong monotonicity, used in the current literature. 相似文献
2.
Shaohua Pan Jein-Shan Chen Sangho Kum Yongdo Lim 《Computational Optimization and Applications》2011,49(3):457-491
In this paper, we study the properties of the penalized Fischer-Burmeister (FB) second-order cone (SOC) complementarity function.
We show that the function possesses similar desirable properties of the FB SOC complementarity function for local convergence;
for example, with the function the second-order cone complementarity problem (SOCCP) can be reformulated as a (strongly) semismooth
system of equations, and the corresponding nonsmooth Newton method has local quadratic convergence without strict complementarity
of solutions. In addition, the penalized FB merit function has bounded level sets under a rather weak condition which can
be satisfied by strictly feasible monotone SOCCPs or SOCCPs with the Cartesian R
01-property, although it is not continuously differentiable. Numerical results are included to illustrate the theoretical considerations. 相似文献
3.
Chuqun Li 《Optimization》2016,65(8):1569-1584
In this paper, we introduce and investigate a constrained mixed set-valued variational inequality (MSVI) in Hilbert spaces. We prove the solution set of the constrained MSVI is a singleton under strict monotonicity. We also propose four merit functions for the constrained MSVI, that is, the natural residual, gap function, regularized gap function and D-gap function. We further use these functions to obtain error bounds, i.e. upper estimates for the distance to solutions of the constrained MSVI under strong monotonicity and Lipschitz continuity. The approach exploited in this paper is based on the generalized f-projection operator due to Wu and Huang, but not the well-known proximal mapping. 相似文献
4.
For the extended linear complementarity problem over an affine subspace, we first study some characterizations of (strong)
column/row monotonicity and (strong) R
0-property. We then establish global s-type error bound for this problem with the column monotonicity or R
0-property, especially for the one with the nondegeneracy and column monotonicity, and give several equivalent formulations
of such error bound without the square root term for monotone affine variational inequality. Finally, we use this error bound
to derive some properties of the iterative sequence produced by smoothing methods for solving such a problem under suitable
assumptions.
Received: May 2, 1999 / Accepted: February 21, 2000?Published online July 20, 2000 相似文献
5.
In this paper, we present a detailed investigation for the properties of a one-parametric class of SOC complementarity functions,
which include the globally Lipschitz continuity, strong semismoothness, and the characterization of their B-subdifferential.
Moreover, for the merit functions induced by them for the second-order cone complementarity problem (SOCCP), we provide a
condition for each stationary point to be a solution of the SOCCP and establish the boundedness of their level sets, by exploiting
Cartesian P-properties. We also propose a semismooth Newton type method based on the reformulation of the nonsmooth system of equations
involving the class of SOC complementarity functions. The global and superlinear convergence results are obtained, and among
others, the superlinear convergence is established under strict complementarity. Preliminary numerical results are reported
for DIMACS second-order cone programs, which confirm the favorable theoretical properties of the method. 相似文献
6.
M. A. Tawhid 《Computational Optimization and Applications》2008,39(1):51-74
This paper deals with nonnegative nonsmooth generalized complementarity problem, denoted by GCP(f,g). Starting with H-differentiable functions f and g, we describe H-differentials of some GCP functions and their merit functions. We show how, under appropriate conditions on H-differentials of f and g, minimizing a merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we generalize the concepts of monotonicity, P
0-property and their variants for functions and use them to establish some conditions to get a solution for generalized complementarity
problem. Our results are generalizations of such results for nonlinear complementarity problem when the underlying functions
are C
1, semismooth, and locally Lipschitzian. 相似文献
7.
In this paper, we extend the one-parametric class of merit functions proposed by Kanzow and Kleinmichel [C. Kanzow, H. Kleinmichel, A new class of semismooth Newton-type methods for nonlinear complementarity problems, Comput. Optim. Appl. 11 (1998) 227-251] for the nonnegative orthant complementarity problem to the general symmetric cone complementarity problem (SCCP). We show that the class of merit functions is continuously differentiable everywhere and has a globally Lipschitz continuous gradient mapping. From this, we particularly obtain the smoothness of the Fischer-Burmeister merit function associated with symmetric cones and the Lipschitz continuity of its gradient. In addition, we also consider a regularized formulation for the class of merit functions which is actually an extension of one of the NCP function classes studied by [C. Kanzow, Y. Yamashita, M. Fukushima, New NCP functions and their properties, J. Optim. Theory Appl. 97 (1997) 115-135] to the SCCP. By exploiting the Cartesian P-properties for a nonlinear transformation, we show that the class of regularized merit functions provides a global error bound for the solution of the SCCP, and moreover, has bounded level sets under a rather weak condition which can be satisfied by the monotone SCCP with a strictly feasible point or the SCCP with the joint Cartesian R02-property. All of these results generalize some recent important works in [J.-S. Chen, P. Tseng, An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Program. 104 (2005) 293-327; C.-K. Sim, J. Sun, D. Ralph, A note on the Lipschitz continuity of the gradient of the squared norm of the matrix-valued Fischer-Burmeister function, Math. Program. 107 (2006) 547-553; P. Tseng, Merit function for semidefinite complementarity problems, Math. Program. 83 (1998) 159-185] under a unified framework. 相似文献
8.
Yoichi Enatsu Eleonora Messina Yukihiko Nakata Yoshiaki Muroya Elvira Russo Antonia Vecchio 《Journal of Applied Mathematics and Computing》2012,39(1-2):15-34
In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays $\int^{h}_{0} p(\tau)f(S(t),I(t-\tau)) \mathrm{d}\tau$ under the condition that the total population converges to 1. By using a technical lemma which is derived from strong condition of strict monotonicity of functions f(S,I) and f(S,I)/I with respect to S??0 and I>0, we extend the global stability result for an SIR epidemic model if R 0>1, where R 0 is the basic reproduction number. By using a limit system of the model, we also show that the disease-free equilibrium is globally asymptotically stable if R 0=1. 相似文献
9.
Eugenia Prez 《Mathematical Methods in the Applied Sciences》2005,28(10):1173-1200
We consider a set of Neumann (mixed, respectively) eigenvalue problems for the Laplace operator. Each problem is posed in a bounded domain ΩR of ?n, with n=2,3, which contains a fixed bounded domain B where the density takes the value 1 and 0 outside. ΩR has a diameter depending on a parameter R, with R?1, diam(ΩR) →∞ as R→∞ and the union of these sets is the whole space ?n (the half space {x∈?n/xn<0}, respectively). Depending on the dimension of the space n, and on the boundary conditions, we describe the asymptotic behaviour of the eigenelements as R→∞. We apply these asymptotics in order to derive important spectral properties for vibrating systems with concentrated masses. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
10.
Luiza A. Moraes 《Results in Mathematics》1981,4(1-2):201-212
We study strict inductive limits of Fréchet Montel (FM) spaces and reflexive Fréchet (RF) spaces and we obtain some interesting examples in the theory of infinite dimensional holomorphy. PM(kE′) and PHY(kE′) will denote respectively the set of all k-homogeneous polynomials on E′ that are bounded on bounded sets and the set of all k-homogeneous polynomials on E′ that are continuous on compact sets. ?SM(kE′) is the space of all symetric k -multilinear mappings from E′ × ... × E′ into C that are bounded on bounded sets. HHY(E′) will denote the set of all G-analytic functions on E′ that are continuous on the compact subsets of E′. 相似文献
11.
H. D. Qi 《Journal of Optimization Theory and Applications》1999,102(2):411-431
Motivated by the work of Fukushima and Pang (Ref. 1), we study the equivalent relationship between minimizing and stationary sequences of a new class of merit functions for nonlinear complementarity problems (NCP). These merit functions generalize that obtained via the squared Fischer–Burmeister NCP function, which was used in Ref. 1. We show that a stationary sequence {xk} /Ren is a minimizing sequence under the condition that the function value sequence {F(x
k)} is bounded above or the Jacobian matrix sequence {F(x
k)} is bounded, where F is the function involved in NCP. The latter condition is also assumed by Fukushima and Pang. The converse is true under the assumption of {F(x
k)} bounded. As an example shows, even for a bounded function F, the boundedness of the sequence {F(x
k)} is necessary for a minimizing sequence to be a stationary sequence. 相似文献
12.
Jie-Cheng Chen 《Israel Journal of Mathematics》1993,81(1-2):193-202
In this paper, we get a necessary and sufficient condition on the weights (μ,v) for the Poisson integral operator to be bounded fromL
Φ(R
n, v(x)dx) to weak-L
Φ(R
+
n+1
,dμ), where Φ is anN-function satisfying the Δ2-condition. We also find a necessary and sufficient condition on the weights (μ,v) for the Poisson integral operator to be bounded fromL
Φ(R
n,v(x)dx) toL
Φ(R
+
n+1
,dμ) under some additional condition.
Partially supported by NNSF of P.R. China 相似文献
13.
Vladimir Maz'ya 《偏微分方程通讯》2013,38(2):191-207
We consider weak solutions of an elliptic equation of the form ? i ? i (a ij u) = 0 and their asymptotic properties at an interior point. We assume that the coefficients are bounded, measurable, complex-valued functions that stabilize as x → 0 in that the norm of the matrix (a ij (x) ? δ ij ) on the annulus B 2r \ B r is bounded by a function Ω(r), where Ω2(r) satisfies the Dini condition at r = 0, as well as some technical monotonicity conditions; under these assumptions, solutions need not be continuous. Our main result is an explicit formula for the leading asymptotic term for solutions with at most a mild singularity at x = 0. As a consequence, we obtain upper and lower estimates for the L p -norm of solutions, as well as necessary and sufficient conditions for solutions to be bounded or tend to zero in L p -mean as r → 0. 相似文献
14.
Xin-He Miao Yu-Lin Chang Jein-Shan Chen 《Computational Optimization and Applications》2017,67(1):155-173
Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving p-order cone complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also assert that these merit functions provide an error bound for the p-order cone complementarity problem. These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem. 相似文献
15.
In this paper we continue with our work in Lederman and Wolanski (Ann Math Pura Appl 187(2):197–220, 2008) where we developed
a local monotonicity formula for solutions to an inhomogeneous singular perturbation problem of interest in combustion theory.
There we proved local monotonicity formulae for solutions ue{{u^\varepsilon}} to the singular perturbation problem and for u=limue{u=\lim{u^\varepsilon}} , assuming that both ue{{u^\varepsilon}} and u were defined in an arbitrary domain D{\mathcal{D}} in
\mathbbRN+1{\mathbb{R}^{N+1}} . In the present work we obtain global monotonicity formulae for limit functions u that are globally defined, while ue{{u^\varepsilon}} are not. We derive such global formulae from a local one that we prove here. In particular, we obtain a global monotonicity
formula for blow up limits u
0 of limit functions u that are not globally defined. As a consequence of this formula, we characterize blow up limits u
0 in terms of the value of a density at the blow up point. We also present applications of the results in this paper to the
study of the regularity of ∂{u > 0} (the flame front in combustion models). The fact that our results hold for the inhomogeneous singular perturbation problem
allows a very wide applicability, for instance to problems with nonlocal diffusion and/or transport. 相似文献
16.
Yu Ding 《Israel Journal of Mathematics》2002,129(1):241-251
In this paper we prove that when the Ricci curvature of a Riemannian manifoldM
n
is almost nonnegative, and a ballB
L
(p)⊂M
n
is close in Gromov-Hausdorff distance to a Euclidean ball, then the gradient of the harmonic functionb defined in [ChCo1] does not vanish. In particular, these functions can serve as harmonic coordinates on balls sufficiently
close to an Euclidean ball. The proof, is based on a monotonicity theorem that generalizes monotonicity of the frequency for
harmonic functions onR
n
. 相似文献
17.
《Optimization》2012,61(8):1173-1197
We consider a class of derivative-free descent methods for solving the second-order cone complementarity problem (SOCCP). The algorithm is based on the Fischer–Burmeister (FB) unconstrained minimization reformulation of the SOCCP, and utilizes a convex combination of the negative partial gradients of the FB merit function ψFB as the search direction. We establish the global convergence results of the algorithm under monotonicity and the uniform Jordan P-property, and show that under strong monotonicity the merit function value sequence generated converges at a linear rate to zero. Particularly, the rate of convergence is dependent on the structure of second-order cones. Numerical comparisons are also made with the limited BFGS method used by Chen and Tseng (An unconstrained smooth minimization reformulation of the second-order cone complementarity problem, Math. Program. 104(2005), pp. 293–327), which confirm the theoretical results and the effectiveness of the algorithm. 相似文献
18.
Summary An open subsetD ofR
d
,d≧2, is called Poissonian iff every bounded harmonic function on the set is a Poisson integral of a bounded function on its boundary.
We show that the intersection of two Poissonian open sets is itself Poissonian and give a sufficient condition for the union
of two Poissonian open sets to be Poissonian. Some necessary and sufficient conditions for an open set to be Poissonian are
also given. In particular, we give a necessary and sufficient condition for a GreenianD to be Poissonian in terms of its Martin boundary.
Supported by NSF DMS86-01800. 相似文献
19.
We study the best constant in the inequality corresponding to the Sobolev embedding W
n,1(R
n
) into the space of bounded continuous functions C
0(R
n
). Then, we adapt this inequality on compact Riemannian manifolds and discuss on its optimality. 相似文献
20.
Jein-Shan Chen 《Mathematical Methods of Operations Research》2006,64(3):495-519
Recently Tseng (Math Program 83:159–185, 1998) extended a class of merit functions, proposed by Luo and Tseng (A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204–225, 1997), for the nonlinear complementarity problem (NCP) to the semidefinite complementarity problem (SDCP) and showed several related properties. In this paper, we extend this class of merit functions to the second-order cone complementarity problem (SOCCP) and show analogous properties as in NCP and SDCP cases. In addition, we study another class of merit functions which are based on a slight modification of the aforementioned class of merit functions. Both classes of merit functions provide an error bound for the SOCCP and have bounded level sets.Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office. The author’s work is partially supported by National Science Council of Taiwan. 相似文献