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Journal articles on the topic 'Analisi nonsmooth'

Author: Grafiati

Published: 11 March 2023

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1

Filippakis, Michael E., and Nikolaos S. Papageorgiou. "Solutions for nonlinear variational inequalities with a nonsmooth potential." Abstract and Applied Analysis 2004, no. 8 (2004): 635–49. http://dx.doi.org/10.1155/s1085337504312017.

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First we examine a resonant variational inequality driven by thep-Laplacian and with a nonsmooth potential. We prove the existence of a nontrivial solution. Then we use this existence theorem to obtain nontrivial positive solutions for a class of resonant elliptic equations involving thep-Laplacian and a nonsmooth potential. Our approach is variational based on the nonsmooth critical point theory for functionals of the formφ=φ1+φ2withφ1locally Lipschitz andφ2proper, convex, lower semicontinuous.

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2

Chen, Yuan-yuan, and Shou-qiang Du. "A New Smoothing Nonlinear Conjugate Gradient Method for Nonsmooth Equations with Finitely Many Maximum Functions." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/780107.

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The nonlinear conjugate gradient method is of particular importance for solving unconstrained optimization. Finitely many maximum functions is a kind of very useful nonsmooth equations, which is very useful in the study of complementarity problems, constrained nonlinear programming problems, and many problems in engineering and mechanics. Smoothing methods for solving nonsmooth equations, complementarity problems, and stochastic complementarity problems have been studied for decades. In this paper, we present a new smoothing nonlinear conjugate gradient method for nonsmooth equations with finitely many maximum functions. The new method also guarantees that any accumulation point of the iterative points sequence, which is generated by the new method, is a Clarke stationary point of the merit function for nonsmooth equations with finitely many maximum functions.

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3

Huang, Ming, Li-Ping Pang, Xi-Jun Liang, and Zun-Quan Xia. "The Space Decomposition Theory for a Class of Semi-Infinite Maximum Eigenvalue Optimizations." Abstract and Applied Analysis 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/845017.

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We study optimization problems involving eigenvalues of symmetric matrices. We present a nonsmooth optimization technique for a class of nonsmooth functions which are semi-infinite maxima of eigenvalue functions. Our strategy uses generalized gradients and𝒰𝒱space decomposition techniques suited for the norm and other nonsmooth performance criteria. For the class of max-functions, which possesses the so-called primal-dual gradient structure, we compute smooth trajectories along which certain second-order expansions can be obtained. We also give the first- and second-order derivatives of primal-dual function in the space of decision variablesRmunder some assumptions.

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4

Qing-Mei, Zhou, and Ge Bin. "Three Solutions for Inequalities Dirichlet Problem Driven byp(x)-Laplacian-Like." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/575328.

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A class of nonlinear elliptic problems driven byp(x)-Laplacian-like with a nonsmooth locally Lipschitz potential was considered. Applying the version of a nonsmooth three-critical-point theorem, existence of three solutions of the problem is proved.

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5

Carl, Siegfried, Robert P. Gilbert, and Dumitru Motreanu. "‘Nonsmooth Variational Problems’." Applicable Analysis 89, no. 2 (February 2010): 159. http://dx.doi.org/10.1080/00036811003637814.

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6

Wang, Yanyong, Yubin Yan, and Yan Yang. "Two high-order time discretization schemes for subdiffusion problems with nonsmooth data." Fractional Calculus and Applied Analysis 23, no. 5 (October 1, 2020): 1349–80. http://dx.doi.org/10.1515/fca-2020-0067.

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Abstract Two new high-order time discretization schemes for solving subdiffusion problems with nonsmooth data are developed based on the corrections of the existing time discretization schemes in literature. Without the corrections, the schemes have only a first order of accuracy for both smooth and nonsmooth data. After correcting some starting steps and some weights of the schemes, the optimal convergence orders O(k 3–α ) and O(k 4–α ) with 0 < α < 1 can be restored for any fixed time t for both smooth and nonsmooth data, respectively. The error estimates for these two new high-order schemes are proved by using Laplace transform method for both homogeneous and inhomogeneous problem. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

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7

Papalini, Francesca. "Nonlinear Periodic Systems with thep-Laplacian: Existence and Multiplicity Results." Abstract and Applied Analysis 2007 (2007): 1–23. http://dx.doi.org/10.1155/2007/80394.

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We study second-order nonlinear periodic systems driven by the vectorp-Laplacian with a nonsmooth, locally Lipschitz potential function. Under minimal and natural hypotheses on the potential and using variational methods based on the nonsmooth critical point theory, we prove existence theorems and a multiplicity result. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite (unbounded from both above and below).

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8

Lewis, A. S. "Lidskii's Theorem via Nonsmooth Analysis." SIAM Journal on Matrix Analysis and Applications 21, no. 2 (January 2000): 379–81. http://dx.doi.org/10.1137/s0895479898338676.

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9

Kandilakis, Dimitrios, and Nikolaos S. Papageorgiou. "Nonsmooth analysis and approximation." Journal of Approximation Theory 52, no. 1 (January 1988): 58–81. http://dx.doi.org/10.1016/0021-9045(88)90037-8.

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10

Shen, Jie, Miao Tian, Fang-Fang Guo, and Jun-Nan Zhang. "A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces." Journal of Function Spaces 2017 (2017): 1–7. http://dx.doi.org/10.1155/2017/3941084.

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A new bundle-type approach for solving a class of functional equations is presented by combining bundle idea for nonsmooth optimization with common iterative process for functional equations. Our strategy is to approximate the nonsmooth function in functional equation by a sequence of convex piecewise linear functions, as in the bundle method; this makes the problem more tractable and reduces the difficulty of implementation of method. We only require the piecewise linear convex approximate functions, rather than the actual function, to satisfy the uniform boundedness condition with respect to one variable at stability centers. One example is given to demonstrate the application of the proposed method.

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11

Huang, Liren, Chunguang Liu, Lulin Tan, and Qi Ye. "Generalized representer theorems in Banach spaces." Analysis and Applications 19, no. 01 (December 3, 2019): 125–46. http://dx.doi.org/10.1142/s0219530519410100.

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In this paper, we generalize the representer theorems in Banach spaces by the theory of nonsmooth analysis. The generalized representer theorems assure that the regularized learning models can be constructed by the nonconvex loss functions, the generalized training data, and the general Banach spaces which are nonreflexive, nonstrictly convex, and nonsmooth. Specially, the sparse representations of the regularized learning in 1-norm reproducing kernel Banach spaces are shown by the generalized representer theorems.

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12

Azagra, D., J. Ferrera, and J. Gómez-Gil. "Nonsmooth Morse–Sard theorems." Nonlinear Analysis 160 (September 2017): 53–69. http://dx.doi.org/10.1016/j.na.2017.05.006.

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13

Degla, Guy, Cyrille Dansou, and Fortuné Dohemeto. "On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces." Abstract and Applied Analysis 2022 (July 28, 2022): 1–19. http://dx.doi.org/10.1155/2022/1021461.

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In this paper, we establish a generalization of the Galewski-Rădulescu nonsmooth global implicit function theorem to locally Lipschitz functions defined from infinite dimensional Banach spaces into Euclidean spaces. Moreover, we derive, under suitable conditions, a series of results on the existence, uniqueness, and possible continuity of global implicit functions that parametrize the set of zeros of locally Lipschitz functions. Our methods rely on a nonsmooth critical point theory based on a generalization of the Ekeland variational principle.

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14

Narushima, Yasushi, Hideho Ogasawara, and Shunsuke Hayashi. "A Smoothing Method with Appropriate Parameter Control Based on Fischer-Burmeister Function for Second-Order Cone Complementarity Problems." Abstract and Applied Analysis 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/830698.

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We deal with complementarity problems over second-order cones. The complementarity problem is an important class of problems in the real world and involves many optimization problems. The complementarity problem can be reformulated as a nonsmooth system of equations. Based on the smoothed Fischer-Burmeister function, we construct a smoothing Newton method for solving such a nonsmooth system. The proposed method controls a smoothing parameter appropriately. We show the global and quadratic convergence of the method. Finally, some numerical results are given.

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15

Yang, Yan, Yubin Yan, and Neville J. Ford. "Some Time Stepping Methods for Fractional Diffusion Problems with Nonsmooth Data." Computational Methods in Applied Mathematics 18, no. 1 (January 1, 2018): 129–46. http://dx.doi.org/10.1515/cmam-2017-0037.

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AbstractWe consider error estimates for some time stepping methods for solving fractional diffusion problems with nonsmooth data in both homogeneous and inhomogeneous cases. McLean and Mustapha [18] established an {O(k)} convergence rate for the piecewise constant discontinuous Galerkin method with nonsmooth initial data for the homogeneous problem when the linear operator A is assumed to be self-adjoint, positive semidefinite and densely defined in a suitable Hilbert space, where k denotes the time step size. In this paper, we approximate the Riemann–Liouville fractional derivative by Diethelm’s method (or L1 scheme) and obtain the same time discretisation scheme as in McLean and Mustapha [18]. We first prove that this scheme has also convergence rate {O(k)} with nonsmooth initial data for the homogeneous problem when A is a closed, densely defined linear operator satisfying some certain resolvent estimates. We then introduce a new time discretisation scheme for the homogeneous problem based on the convolution quadrature and prove that the convergence rate of this new scheme is {O(k^{1+\alpha})}, {0<\alpha<1}, with the nonsmooth initial data. Using this new time discretisation scheme for the homogeneous problem, we define a time stepping method for the inhomogeneous problem and prove that the convergence rate of this method is {O(k^{1+\alpha})}, {0<\alpha<1}, with the nonsmooth data. Numerical examples are given to show that the numerical results are consistent with the theoretical results.

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16

Karmitsa, Napsu, and Sona Taheri. "Special Issue “Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov”: Foreword by Guest Editors." Algorithms 13, no. 11 (November 7, 2020): 282. http://dx.doi.org/10.3390/a13110282.

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Nonsmooth optimization refers to the general problem of minimizing (or maximizing) functions that have discontinuous gradients. This Special Issue contains six research articles that collect together the most recent techniques and applications in the area of nonsmooth optimization. These include novel techniques utilizing some decomposable structures in nonsmooth problems—for instance, the difference-of-convex (DC) structure—and interesting important practical problems, like multiple instance learning, hydrothermal unit-commitment problem, and scheduling the disposal of nuclear waste.

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17

Yuan, Gonglin, and Zengxin Wei. "THE BARZILAI AND BORWEIN GRADIENT METHOD WITH NONMONOTONE LINE SEARCH FOR NONSMOOTH CONVEX OPTIMIZATION PROBLEMS." Mathematical Modelling and Analysis 17, no. 2 (April 1, 2012): 203–16. http://dx.doi.org/10.3846/13926292.2012.661375.

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The Barzilai and Borwein gradient algorithm has received a great deal of attention in recent decades since it is simple and effective for smooth optimization problems. Whether can it be extended to solve nonsmooth problems? In this paper, we answer this question positively. The Barzilai and Borwein gradient algorithm combined with a nonmonotone line search technique is proposed for nonsmooth convex minimization. The global convergence of the given algorithm is established under suitable conditions. Numerical results show that this method is efficient.

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18

Gao, Dongdong, and Jianli Li. "Three Solutions for Fourth-Order Impulsive Differential Inclusions via Nonsmooth Critical Point Theory." Journal of Function Spaces 2018 (September 6, 2018): 1–9. http://dx.doi.org/10.1155/2018/1871453.

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An existence of at least three solutions for a fourth-order impulsive differential inclusion will be obtained by applying a nonsmooth version of a three-critical-point theorem. Our results generalize and improve some known results.

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19

Craven, B. D. "Nonsmooth multiobjective programming." Numerical Functional Analysis and Optimization 10, no. 1-2 (January 1989): 49–64. http://dx.doi.org/10.1080/01630568908816290.

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20

Gwinner, J. "Three-Field Modelling of Nonlinear Nonsmooth Boundary Value Problems and Stability of Differential Mixed Variational Inequalities." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/108043.

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The purpose of this paper is twofold. Firstly we consider nonlinear nonsmooth elliptic boundary value problems, and also related parabolic initial boundary value problems that model in a simplified way steady-state unilateral contact with Tresca friction in solid mechanics, respectively, stem from nonlinear transient heat conduction with unilateral boundary conditions. Here a recent duality approach, that augments the classical Babuška-Brezzi saddle point formulation for mixed variational problems to twofold saddle point formulations, is extended to the nonsmooth problems under consideration. This approach leads to variational inequalities of mixed form for three coupled fields as unknowns and to related differential mixed variational inequalities in the time-dependent case. Secondly we are concerned with the stability of the solution set of a general class of differential mixed variational inequalities. Here we present a novel upper set convergence result with respect to perturbations in the data, including perturbations of the associated nonlinear maps, the nonsmooth convex functionals, and the convex constraint set. We employ epiconvergence for the convergence of the functionals and Mosco convergence for set convergence. We impose weak convergence assumptions on the perturbed maps using the monotonicity method of Browder and Minty.

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21

Kornev, S. V., and V. V. Obukhovskii. "On Nonsmooth Multivalent Guiding Functions." Differential Equations 39, no. 11 (November 2003): 1578–84. http://dx.doi.org/10.1023/b:dieq.0000019349.33172.ee.

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22

Fan, Liya. "Generalized invexity of nonsmooth functions." Nonlinear Analysis: Theory, Methods & Applications 69, no. 11 (December 2008): 4190–98. http://dx.doi.org/10.1016/j.na.2007.10.047.

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23

Ward, Doug. "Chain rules for nonsmooth functions." Journal of Mathematical Analysis and Applications 158, no. 2 (July 1991): 519–38. http://dx.doi.org/10.1016/0022-247x(91)90254-w.

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24

Pourciau, Bruce. "Global invertibility of nonsmooth mappings." Journal of Mathematical Analysis and Applications 131, no. 1 (April 1988): 170–79. http://dx.doi.org/10.1016/0022-247x(88)90198-9.

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25

Stechlinski, Peter, and Paul I. Barton. "Nonsmooth Hessenberg differential-algebraic equations." Journal of Mathematical Analysis and Applications 495, no. 1 (March 2021): 124721. http://dx.doi.org/10.1016/j.jmaa.2020.124721.

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26

Delfour, M. C., and J. P. Zolésio. "Structure of shape derivatives for nonsmooth domains." Journal of Functional Analysis 104, no. 1 (February 1992): 1–33. http://dx.doi.org/10.1016/0022-1236(92)90087-y.

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27

Kozlov, Vladimir. "On the Hadamard formula for nonsmooth domains." Journal of Differential Equations 230, no. 2 (November 2006): 532–55. http://dx.doi.org/10.1016/j.jde.2006.08.004.

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28

Papageorgiou, Nikolaus S., and Dimitrios A. Kandilakis. "Convergence in approximation and nonsmooth analysis." Journal of Approximation Theory 49, no. 1 (January 1987): 41–54. http://dx.doi.org/10.1016/0021-9045(87)90112-2.

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29

Bacciotti, A., and F. Ceragioli. "Nonsmooth optimal regulation and discontinuous stabilization." Abstract and Applied Analysis 2003, no. 20 (2003): 1159–95. http://dx.doi.org/10.1155/s1085337503304014.

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For affine control systems, we study the relationship between an optimal regulation problem on the infinite horizon and stabilizability. We are interested in the case the value function of the optimal regulation problem is not smooth and feedback laws involved in stabilizability may be discontinuous.

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30

Ansari, Qamrul Hasan, Monirul Islam, and Jen-Chih Yao. "Nonsmooth variational inequalities on Hadamard manifolds." Applicable Analysis 99, no. 2 (August 1, 2018): 340–58. http://dx.doi.org/10.1080/00036811.2018.1495329.

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31

Páles, Zsolt. "Optimum problems with nonsmooth equality constraints." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): e2575-e2581. http://dx.doi.org/10.1016/j.na.2004.10.005.

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32

Liu, Jiaquan, and Yuxia Guo. "Critical point theory for nonsmooth functionals." Nonlinear Analysis: Theory, Methods & Applications 66, no. 12 (June 2007): 2731–41. http://dx.doi.org/10.1016/j.na.2006.04.003.

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33

Vasundhara Devi, J., and V. Lakshmikantham. "Nonsmooth analysis and fractional differential equations." Nonlinear Analysis: Theory, Methods & Applications 70, no. 12 (June 2009): 4151–57. http://dx.doi.org/10.1016/j.na.2008.09.003.

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34

Gürbüzbalaban, Mert, and Michael L. Overton. "On Nesterov’s nonsmooth Chebyshev–Rosenbrock functions." Nonlinear Analysis: Theory, Methods & Applications 75, no. 3 (February 2012): 1282–89. http://dx.doi.org/10.1016/j.na.2011.07.062.

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35

Gowda, M. Seetharama, and G. Ravindran. "Algebraic Univalence Theorems for Nonsmooth Functions." Journal of Mathematical Analysis and Applications 252, no. 2 (December 2000): 917–35. http://dx.doi.org/10.1006/jmaa.2000.7171.

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36

Kas̀kosz, Barbara, and Stanisław Łojasiewicz. "On a nonconvex, nonsmooth control system." Journal of Mathematical Analysis and Applications 136, no. 1 (November 1988): 39–53. http://dx.doi.org/10.1016/0022-247x(88)90114-x.

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37

Soleimani-damaneh, M., and G. R. Jahanshahloo. "Nonsmooth multiobjective optimization using limiting subdifferentials." Journal of Mathematical Analysis and Applications 328, no. 1 (April 2007): 281–86. http://dx.doi.org/10.1016/j.jmaa.2006.05.026.

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38

Chan, C. Y., and L. Ke. "Parabolic Quenching for Nonsmooth Convex Domains." Journal of Mathematical Analysis and Applications 186, no. 1 (August 1994): 52–65. http://dx.doi.org/10.1006/jmaa.1994.1285.

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39

Al-Nayef, A. A., P. E. Kloeden, and A. V. Pokrovskii. "Expansivity of Nonsmooth Functional Differential Equations." Journal of Mathematical Analysis and Applications 208, no. 2 (April 1997): 453–61. http://dx.doi.org/10.1006/jmaa.1997.5337.

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40

Lei, Chun-Yu, and Jia-Feng Liao. "Positive radial symmetric solutions for a class of elliptic problems with critical exponent and -1 growth." Advances in Nonlinear Analysis 10, no. 1 (January 1, 2021): 1222–34. http://dx.doi.org/10.1515/anona-2020-0174.

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Abstract In this paper, we consider a class of semilinear elliptic equation with critical exponent and -1 growth. By using the critical point theory for nonsmooth functionals, two positive solutions are obtained. Moreover, the symmetry and monotonicity properties of the solutions are proved by the moving plane method. Our results improve the corresponding results in the literature.

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41

Teng, Kaimin. "Infinitely Many Solutions for a Class of Fractional Boundary Value Problems with Nonsmooth Potential." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/181052.

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We establish the existence of infinitely many solutions for a class of fractional boundary value problems with nonsmooth potential. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.

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42

Ferrara, Massimiliano, Giuseppe Caristi, and Amjad Salari. "Existence of Infinitely Many Periodic Solutions for Perturbed Semilinear Fourth-Order Impulsive Differential Inclusions." Abstract and Applied Analysis 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/5784273.

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This paper discusses the existence of infinitely many periodic solutions for a semilinear fourth-order impulsive differential inclusion with a perturbed nonlinearity and two parameters. The approach is based on a critical point theorem for nonsmooth functionals.

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43

Fowler, K. R., and C. T. Kelley. "Pseudo-Transient Continuation for Nonsmooth Nonlinear Equations." SIAM Journal on Numerical Analysis 43, no. 4 (January 2005): 1385–406. http://dx.doi.org/10.1137/s0036142903431298.

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44

Chen, Dongxiang, Dan Zou, and Suzhen Mao. "Multiple Weighted Estimates for Vector-Valued Multilinear Singular Integrals with Non-Smooth Kernels and Its Commutators." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/363916.

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This note concerns multiple weighted inequalities for vector-valued multilinear singular integral operator with nonsmooth kernel and its corresponding commutators containing multilinear commutator and iterated commutator generated by the vector-valued multilinear operator and BMO functions. By the weighted estimates for a class of new variant maximal and sharp maximal functions, the multiple weighted norm inequalities for such operators are obtained.

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45

Ge, Bin, and Ji-Hong Shen. "Multiple Solutions for a Class of Differential Inclusion System Involving the(p(x),q(x))-Laplacian." Abstract and Applied Analysis 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/971243.

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We consider a differential inclusion system involving the(p(x),q(x))-Laplacian with Dirichlet boundary condition on a bounded domain and obtain two nontrivial solutions under appropriate hypotheses. Our approach is variational and it is based on the nonsmooth critical point theory for locally Lipschitz functions.

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46

Grubb, Gerd. "Spectral Asymptotics for Nonsmooth Singular Green Operators." Communications in Partial Differential Equations 39, no. 3 (February 10, 2014): 530–73. http://dx.doi.org/10.1080/03605302.2013.864207.

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47

Mishra, S. K., G. Giorgi, and K. K. Lai. "On nonsmooth multiobjective programming with generalized univexity." Journal of Interdisciplinary Mathematics 10, no. 5 (October 2007): 681–95. http://dx.doi.org/10.1080/09720502.2007.10700525.

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48

Lassonde, Marc. "First-order rules for nonsmooth constrained optimization." Nonlinear Analysis: Theory, Methods & Applications 44, no. 8 (June 2001): 1031–56. http://dx.doi.org/10.1016/s0362-546x(99)00321-1.

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49

Soleimani-damaneh, M. "Optimality for nonsmooth fractional multiple objective programming." Nonlinear Analysis: Theory, Methods & Applications 68, no. 10 (May 2008): 2873–78. http://dx.doi.org/10.1016/j.na.2007.02.033.

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50

Lomov, I. S. "Nonsmooth eigenfunctions in problems of mathematical physics." Differential Equations 47, no. 3 (March 2011): 355–62. http://dx.doi.org/10.1134/s0012266111030062.

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