Готові списки джерел за темами / Analisi nonsmooth

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Добірка наукової літератури з теми "Analisi nonsmooth"

Автор: Grafiati
Опубліковано: 11 березня 2023

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Статті в журналах з теми "Analisi nonsmooth"

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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Анотація:
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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Анотація:
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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Анотація:
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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Анотація:
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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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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Анотація:
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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Дисертації з теми "Analisi nonsmooth"

1

CASTELPIETRA, MARCO. "Metric, geometric and measure theoretic properties of nonsmooth value functions." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2007. http://hdl.handle.net/2108/202601.

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La funzione valore è un nodo centrale del controllo ottimo. `E noto che la funzione valore può essere irregolare anche per sistemi molto regolari. Pertanto l’analisi non liscia diviene un importante strumento per studiarne le proprietà, anche grazie alle numerose connessioni con la semiconcavità. Sotto opportune ipotesi, la funzione valore è localmente semiconcava. Questa proprietà è connessa anche con la proprietà di sfera interna dei suoi insiemi di livello e dei loro perimetri. In questa tesi introduciamo l’analisi non-liscia e le sue connessioni con funzioni semiconcave ed insiemi di perimetro finito. Descriviamo i sistemi di controllo ed introduciamo le proprietà basilari della funzione tempo minimo T(x) e della funzione valore V (x). Usando il principio del massimo, estendiamo alcuni risultati noti di sfera interna per gli insiemi raggiungibili A(T), al caso non-autonomo ed ai sistemi con costo corrente non costante. Questa proprietà ci permette di ottenere delle stime sui perimetri per alcuni sistemi di controllo. Infine queste proprietà degli insiemi raggiungibili possono essere estese agli insiemi di livello della funzione valore, e, sotto alcune ipotesi di controllabilità otteniamo anche semiconcavità locale per V (x). Inoltre studiamo anche sistemi di controllo vincolati. Nei sistemi vincolati la funzione valore perde regolarità. Infatti, quando una traiettoria tocca il bordo del vincolo Ω, si presentano delle singolarità. Questi effetti sono evidenziati anche dal principio del massimo, che produce un termine aggiuntivo di misura(eventualmente discontinuo), quando una traiettoria tocca il bordo ∂Ω. E la funzione valore perde la semiconcavità, anche per sistemi particolarmente semplici. Ma siamo in grado di recuperare lipschitzianità per il tempo minimo, ed enunciare il principio del massimo esplicitando il termine di bordo. In questo modo otteniamo delle particolari proprietà di sfera interna, e quindi anche stime sui perimetri, per gli insiemi raggiungibili.
The value function is a focal point in optimal control theory. It is a known fact that the value function can be nonsmooth even with very smooth data. So, nonsmooth analysis is a useful tool to study its regularity. Semiconcavity is a regularity property, with some fine connection with nonsmooth analysis. Under appropriate assumptions, the value function is locally semiconcave. This property is connected with the interior sphere property of its level sets and their perimeters. In this thesis we introduce basic concepts of nonsmooth analysis and their connections with semiconcave functions, and sets of finite perimeter. We describe control systems, and we introduce the basic properties of the minimum time function T(x) and of the value function V (x). Then, using maximum principle, we extend some known results of interior sphere property for the attainable setsA(t), to the nonautonomous case and to systems with nonconstant running cost L. This property allow us to obtain some fine perimeter estimates for some class of control systems. Finally these regularity properties of the attainable sets can be extended to the level sets of the value function, and, with some controllability assumption, we also obtain a local semiconcavity for V (x). Moreoverwestudycontrolsystemswithstateconstraints. Inconstrained systems we loose many of regularity properties related to the value function. In fact, when a trajectory of control system touches the boundary of the constraint set Ω, some singularity effect occurs. This effect is clear even in the statement of the maximum principle. Indeed, due to the times in which a trajectory stays on ∂Ω, a measure boundary term (possibly, discontinuous) appears. So, we have no more semiconcavity for the value function, even for very simple control systems. But we recover Lipschitz continuity for the minimum time and we rewrite the constrained maximum principle with an explicit boundary term. We also obtain a kind of interior sphere property, and perimeter estimates for the attainable sets for some class of control systems.
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2

Nguyen, Khai/T. "The regularity of the minimum time function via nonsmooth analysis and geometric measure theory." Doctoral thesis, Università degli studi di Padova, 2010. http://hdl.handle.net/11577/3427404.

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Several regularity results on the minimum time function are proved, together with regularity properties of a class of continuous functions whose hypograph satisfies an external sphere condition.
Si dimostrano risultati di regolarita' per la funzione tempo minimo, mediante particolari proprieta' di una classe di funzioni continue il cui ipografico soddisfa una condizione di sfera esterna.
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3

Soukhoroukova, Nadejda. "Data classification through nonsmooth optimization." Thesis, University of Ballarat [Mt. Helen, Vic.] :, 2003. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/42220.

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4

Mankau, Jan Peter. "A Nonsmooth Nonconvex Descent Algorithm." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-217556.

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Анотація:
In many applications nonsmooth nonconvex energy functions, which are Lipschitz continuous, appear quite naturally. Contact mechanics with friction is a classic example. A second example is the 1-Laplace operator and its eigenfunctions. In this work we will give an algorithm such that for every locally Lipschitz continuous function f and every sequence produced by this algorithm it holds that every accumulation point of the sequence is a critical point of f in the sense of Clarke. Here f is defined on a reflexive Banach space X, such that X and its dual space X' are strictly convex and Clarkson's inequalities hold. (E.g. Sobolev spaces and every closed subspace equipped with the Sobolev norm satisfy these assumptions for p>1.) This algorithm is designed primarily to solve variational problems or their high dimensional discretizations, but can be applied to a variety of locally Lipschitz functions. In elastic contact mechanics the strain energy is often smooth and nonconvex on a suitable domain, while the contact and the friction energy are nonsmooth and have a support on a subspace which has a substantially smaller dimension than the strain energy, since all points in the interior of the bodies only have effect on the strain energy. For such elastic contact problems we suggest a specialization of our algorithm, which treats the smooth part with Newton like methods. In the case that the gradient of the entire energy function is semismooth close to the minimizer, we can even prove superlinear convergence of this specialization of our algorithm. We test the algorithm and its specialization with a couple of benchmark problems. Moreover, we apply the algorithm to the 1-Laplace minimization problem restricted to finitely dimensional subspaces of piecewise affine, continuous functions. The algorithm developed here uses ideas of the bundle trust region method by Schramm, and a new generalization of the concept of gradients on a set. The basic idea behind this gradients on sets is that we want to find a stable descent direction, which is a descent direction on an entire neighborhood of an iteration point. This way we avoid oscillations of the gradients and very small descent steps (in the smooth and in the nonsmooth case). It turns out, that the norm smallest element of the gradient on a set provides a stable descent direction. The algorithm we present here is the first algorithm which can treat locally Lipschitz continuous functions in this generality, up to our knowledge. In particular, large finitely dimensional Banach spaces haven't been studied for nonsmooth nonconvex functions so far. We will show that the algorithm is very robust and often faster than common algorithms. Furthermore, we will see that with this algorithm it is possible to compute reliably the first eigenfunctions of the 1-Laplace operator up to disretization errors, for the first time
In vielen Anwendungen tauchen nichtglatte, nichtkonvexe, Lipschitz-stetige Energie Funktionen in natuerlicher Weise auf. Ein klassische Beispiel bildet die Kontaktmechanik mit Reibung. Ein weiteres Beispiel ist der $1$-Laplace Operator und seine Eigenfunktionen. In dieser Dissertation werden wir ein Abstiegsverfahren angeben, so dass fuer jede lokal Lipschitz-stetige Funktion f jeder Haeufungspunkt einer durch dieses Verfahren erzeugten Folge ein kritischer Punkt von f im Sinne von Clarke ist. Hier ist f auf einem einem reflexiver, strikt konvexem Banachraum definierert, fuer den der Dualraum ebenfalls strikt konvex ist und die Clarkeson Ungleichungen gelten. (Z.B. Sobolevraeume und jeder abgeschlossene Unterraum mit der Sobolevnorm versehen, erfuellt diese Bedingung fuer p>1.) Dieser Algorithmus ist primaer entwickelt worden um Variationsprobleme, bzw. deren hochdimensionalen Diskretisierungen zu loesen. Er kann aber auch fuer eine Vielzahl anderer lokal Lipschitz stetige Funktionen eingesetzt werden. In der elastischen Kontaktmechanik ist die Spannungsenergie oft glatt und nichtkonvex auf einem geeignetem Definitionsbereich, waehrend der Kontakt und die Reibung durch nicht glatte Funktionen modelliert werden, deren Traeger ein Unterraum mit wesentlich kleineren Dimension ist, da alle Punkte im Inneren des Koerpers nur die Spannungsenergie beeinflussen. Fuer solche elastischen Kontaktprobleme schlagen wir eine Spezialisierung unseres Algorithmuses vor, der den glatten Teil mit Newton aehnlichen Methoden behandelt. Falls der Gradient der gesamten Energiefunktion semiglatt in der Naehe der Minimalstelle ist, koennen wir sogar beweisen, dass der Algorithmus superlinear konvergiert. Wir testen den Algorithmus und seine Spezialisierung an mehreren Benchmark Problemen. Ausserdem wenden wir den Algorithmus auf 1-Laplace Minimierungsproblem eingeschraenkt auf eine endlich dimensionalen Unterraum der stueckweise affinen, stetigen Funktionen an. Der hier entwickelte Algorithmus verwendet Ideen des Bundle-Trust-Region-Verfahrens von Schramm, und einen neu entwickelten Verallgemeinerung von Gradienten auf Mengen. Die zentrale Idee hinter den Gradienten auf Mengen ist die, dass wir stabile Abstiegsrichtungen auf einer ganzen Umgebung der Iterationspunkte finden wollen. Auf diese Weise vermeiden wir das Oszillieren der Gradienten und sehr kleine Abstiegsschritte (im glatten, wie im nichtglatten Fall.) Es stellt sich heraus, dass das normkleinste Element dieses Gradienten auf der Umgebung eine stabil Abstiegsrichtung bestimmt. So weit es uns bekannt ist, koennen die hier entwickelten Algorithmen zum ersten Mal lokal Lipschitz-stetige Funktionen in dieser Allgemeinheit behandeln. Insbesondere wurden nichtglatte, nichtkonvexe Funktionen auf derart hochdimensionale Banachraeume bis jetzt nicht behandelt. Wir werden zeigen, dass unser Algorithmus sehr robust und oft schneller als uebliche Algorithmen ist. Des Weiteren, werden wir sehen, dass es mit diesem Algorithmus das erste mal moeglich ist, zuverlaessig die erste Eigenfunktion des 1-Laplace Operators bis auf Diskretisierungsfehler zu bestimmen
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5

Mirzayeva, Hijran. "Nonsmooth optimization algorithms for clusterwise linear regression." Thesis, University of Ballarat, 2013. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/41975.

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Data mining is about solving problems by analyzing data that present in databases. Supervised and unsupervised data classification (clustering) are among the most important techniques in data mining. Regression analysis is the process of fitting a function (often linear) to the data to discover how one or more variables vary as a function of another. The aim of clusterwise regression is to combine both of these techniques, to discover trends within data, when more than one trend is likely to exist. Clusterwise regression has applications for instance in market segmentation, where it allows one to gather information on customer behaviors for several unknown groups of customers. There exist different methods for solving clusterwise linear regression problems. In spite of that, the development of efficient algorithms for solving clusterwise linear regression problems is still an important research topic. In this thesis our aim is to develop new algorithms for solving clusterwise linear regression problems in large data sets based on incremental and nonsmooth optimization approaches. Three new methods for solving clusterwise linear regression problems are developed and numerically tested on publicly available data sets for regression analysis. The first method is a new algorithm for solving the clusterwise linear regression problems based on their nonsmooth nonconvex formulation. This is an incremental algorithm. The second method is a nonsmooth optimization algorithm for solving clusterwise linear regression problems. Nonsmooth optimization techniques are proposed to use instead of the Sp¨ath algorithm to solve optimization problems at each iteration of the incremental algorithm. The discrete gradient method is used to solve nonsmooth optimization problems at each iteration of the incremental algorithm. This approach allows one to reduce the CPU time and the number of regression problems solved in comparison with the first incremental algorithm. The third algorithm is an algorithm based on an incremental approach and on the smoothing techniques for solving clusterwise linear regression problems. The use of smoothing techniques allows one to apply powerful methods of smooth nonlinear programming to solve clusterwise linear regression problems. Numerical results are presented for all three algorithms using small to large data sets. The new algorithms are also compared with multi-start Sp¨ath algorithm for clusterwise linear regression.
Doctor of Philosophy
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6

Mohebi, Ehsan. "Nonsmooth optimization models and algorithms for data clustering and visualization." Thesis, Federation University Australia, 2015. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/77001.

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Cluster analysis deals with the problem of organization of a collection of patterns into clusters based on a similarity measure. Various distance functions can be used to define this measure. Clustering problems with the similarity measure defined by the squared Euclidean distance have been studied extensively over the last five decades. However, problems with other Minkowski norms have attracted significantly less attention. The use of different similarity measures may help to identify different cluster structures of a data set. This in turn may help to significantly improve the decision making process. High dimensional data visualization is another important task in the field of data mining and pattern recognition. To date, the principal component analysis and the self-organizing maps techniques have been used to solve such problems. In this thesis we develop algorithms for solving clustering problems in large data sets using various similarity measures. Such similarity measures are based on the squared L
Doctor of Philosophy
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7

Chen, Jein-Shan. "Merit functions and nonsmooth functions for the second-order cone complementarity problem /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/5782.

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8

Akteke-ozturk, Basak. "New Approaches To Desirability Functions By Nonsmooth And Nonlinear Optimization." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612649/index.pdf.

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Desirability Functions continue to attract attention of scientists and researchers working in the area of multi-response optimization. There are many versions of such functions, differing mainly in formulations of individual and overall desirability functions. Derringer and Suich&rsquo
s desirability functions being used throughout this thesis are still the most preferred ones in practice and many other versions are derived from these. On the other hand, they have a drawback of containing nondifferentiable points and, hence, being nonsmooth. Current approaches to their optimization, which are based on derivative-free search techniques and modification of the functions by higher-degree polynomials, need to be diversified considering opportunities offered by modern nonlinear (global) optimization techniques and related softwares. A first motivation of this work is to develop a new efficient solution strategy for the maximization of overall desirability functions which comes out to be a nonsmooth composite constrained optimization problem by nonsmooth optimization methods. We observe that individual desirability functions used in practical computations are of mintype, a subclass of continuous selection functions. To reveal the mechanism that gives rise to a variation in the piecewise structure of desirability functions used in practice, we concentrate on a component-wise and generically piecewise min-type functions and, later on, max-type functions. It is our second motivation to analyze the structural and topological properties of desirability functions via piecewise max-type functions. In this thesis, we introduce adjusted desirability functions based on a reformulation of the individual desirability functions by a binary integer variable in order to deal with their piecewise definition. We define a constraint on the binary variable to obtain a continuous optimization problem of a nonlinear objective function including nondifferentiable points with the constraints of bounds for factors and responses. After describing the adjusted desirability functions on two well-known problems from the literature, we implement modified subgradient algorithm (MSG) in GAMS incorporating to CONOPT solver of GAMS software for solving the corresponding optimization problems. Moreover, BARON solver of GAMS is used to solve these optimization problems including adjusted desirability functions. Numerical applications with BARON show that this is a more efficient alternative solution strategy than the current desirability maximization approaches. We apply negative logarithm to the desirability functions and consider the properties of the resulting functions when they include more than one nondifferentiable point. With this approach we reveal the structure of the functions and employ the piecewise max-type functions as generalized desirability functions (GDFs). We introduce a suitable finite partitioning procedure of the individual functions over their compact and connected interval that yield our so-called GDFs. Hence, we construct GDFs with piecewise max-type functions which have efficient structural and topological properties. We present the structural stability, optimality and constraint qualification properties of GDFs using that of max-type functions. As a by-product of our GDF study, we develop a new method called two-stage (bilevel) approach for multi-objective optimization problems, based on a separation of the parameters: in y-space (optimization) and in x-space (representation). This approach is about calculating the factor variables corresponding to the ideal solutions of each individual functions in y, and then finding a set of compromised solutions in x by considering the convex hull of the ideal factors. This is an early attempt of a new multi-objective optimization method. Our first results show that global optimum of the overall problem may not be an element of the set of compromised solution. The overall problem in both x and y is extended to a new refined (disjunctive) generalized semi-infinite problem, herewith analyzing the stability and robustness properties of the objective function. In this course, we introduce the so-called robust optimization of desirability functions for the cases when response models contain uncertainty. Throughout this thesis, we give several modifications and extensions of the optimization problem of overall desirability functions.
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9

Piiroinen, Petri. "Recurrent dynamics of nonsmooth systems with application to human gait." Doctoral thesis, KTH, Mechanics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3430.

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10

Ganjehlou, Asef Nazari. "Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis." Thesis, University of Ballarat, 2009. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/59243.

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Книги з теми "Analisi nonsmooth"

1

Optimization and nonsmooth analysis. Philadelphia: SIAM, 1990.

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2

1923-, Moreau Jean-Jacques, Panagiotopoulos P. D. 1950-, and Strang Gilbert, eds. Topics in nonsmooth mechanics. Basel [Switzerland]: Birkhäuser Verlag, 1988.

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3

service), SpringerLink (Online, ed. Topological Aspects of Nonsmooth Optimization. New York, NY: Springer Science+Business Media, LLC, 2012.

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4

International School of Mathematics (4th 1988 Erice, Italy). Nonsmooth optimization and related topics. New York: Plenum Press, 1989.

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5

Course of the International School of Mathematics on Nonsmooth Optimization and Related Topics (4th 1988 Erice, Sicily, Italy). Nonsmooth optimization and related topics. New York: Plenum, 1989.

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6

Methods of dynamic and nonsmooth optimization. Philadelphia, Pa: Society for Industrial and Applied Mathematics, 1989.

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7

Topological aspects of nonsmooth optimization: Ludwig Kuntz. Hamburg: Lit, 1996.

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8

Nonsmooth mechanics and convex optimization. Boca Raton, FL: CRC Press/Taylor & Francis, 2011.

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9

Yang, Gao David, Ogden R. W. 1943-, and Stavroulakis G. E, eds. Nonsmooth/nonconvex mechanics: Modeling, analysis, and numerical methods. Dordrecht: Kluwer Academic Publishers, 2001.

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10

Socrates, Papageorgiou Nikolaos, ed. Nonsmooth critical point theory and nonlinear boundary value problems. Boca Raton, Fla: CRC Press, 2005.

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Частини книг з теми "Analisi nonsmooth"

1

Motreanu, Dumitru, Viorica Venera Motreanu, and Nikolaos Papageorgiou. "Nonsmooth Analysis." In Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 45–59. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9323-5_3.

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2

Vinter, Richard. "Nonsmooth Analysis." In Optimal Control, 127–77. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-8086-2_4.

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3

Dem’yanov, Vladimir F., Georgios E. Stavroulakis, Ludmila N. Polyakova, and Panagiotis D. Panagiotopoulos. "Nonsmooth Analysis." In Nonconvex Optimization and Its Applications, 1–48. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4615-4113-4_1.

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Smirnov, Georgi. "Nonsmooth analysis." In Graduate Studies in Mathematics, 65–84. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/gsm/041/03.

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5

Denkowski, Zdzisław, Stanisław Migórski, and Nikolas S. Papageorgiou. "Nonsmooth Analysis." In An Introduction to Nonlinear Analysis: Theory, 517–664. Boston, MA: Springer US, 2003. http://dx.doi.org/10.1007/978-1-4419-9158-4_5.

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Borwein, Jonathan M., and Adrian S. Lewis. "Nonsmooth Optimization." In Convex Analysis and Nonlinear Optimization, 123–52. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4757-9859-3_6.

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Bounkhel, Messaoud. "Nonsmooth Concepts." In Regularity Concepts in Nonsmooth Analysis, 3–30. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-1019-5_1.

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8

Gasiński, Leszek, and Nikolaos S. Papageorgiou. "Smooth and Nonsmooth Calculus." In Exercises in Analysis, 409–616. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27817-9_3.

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9

Dontchev, Asen L. "Nonsmooth Inverse Function Theorems." In Lectures on Variational Analysis, 97–101. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79911-3_10.

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Shikhman, Vladimir. "Impacts on Nonsmooth Analysis." In Topological Aspects of Nonsmooth Optimization, 167–74. New York, NY: Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4614-1897-9_6.

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Тези доповідей конференцій з теми "Analisi nonsmooth"

1

Matrosov, Alexander V., and Dmitriy P. Goloskokov. "Analysis of elastic systems with nonsmooth boundaries." In 2017 Constructive Nonsmooth Analysis and Related Topics (CNSA). IEEE, 2017. http://dx.doi.org/10.1109/cnsa.2017.7973987.

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2

Sahiner, Ahmet, Havva Gokkaya, and Tuba Yigit. "A new filled function for nonsmooth global optimization." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756304.

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3

Fancello, Matteo, Pierangelo Masarati, and Marco Morandini. "Adding Non-Smooth Analysis Capabilities to General-Purpose Multibody Dynamics by Co-Simulation." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12208.

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Анотація:
Multi-rigid-body dynamics problems with unilateral constraints, like frictionless and frictional contacts, are characterized by nonsmooth dynamics. The issue of nonsmoothness can be addressed with methods that apply a mathematical regularization, called continuous contact methods; alternatively, hard constraints with complementarity approaches can be proficiently used. This work presents an attempt at integrating consistently modeled unilateral constraints in a general purpose multibody formulation and implementation originally designed to address intrinsically smooth problems. The focus is on the analysis of generally smooth problems, characterized by significant multidisciplinarity, with the need to selectively include nonsmooth events localized in time and in specific components of the model. A co-simulation approach between the smooth Differential-Algebraic Equations solver and the classic Moreau-Jean timestepping approach is devised as an alternative to entirely redesigning a monolithic nonsmooth solver, in order to provide elements subject to frictionless and frictional contact in the general-purpose, free multibody solver MBDyn. The implementation uses components from the INRIA’s Siconos library for the solution of Complementarity Problems. The proposed approach is applied to several problems of increasing complexity to empirically evaluate its properties and versatility. The applicability of the family of second-order accurate, A/L stable multistep integration algorithms used by MBDyn to nonsmooth dynamics is also discussed and assessed.
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4

Hinrichs, N., M. Oestreich, and K. Popp. "Friction Induced Vibrations: Experiments, Modelling and Analysis." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-3908.

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Abstract In the present paper, the dynamics of a nonsmooth friction oscillator under self and external excitation is investigated. The rich bifurcational behaviour predicted by numerical simulations is compared to experimental results. In order to predict the period and amplitude of the friction induced vibrations, the friction force can be modeled by means of friction characteristics. A more detailed look at the nonsmooth transition points of the trajectories shows that an extension of the friction model is necessary. For that aim, a bristle model, a friction contact with tangential stiffness and damping and a stochastic friction model are investigated.
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5

Ivanov, Gennady, Gennady Alferov, and Polina Efimova. "Integrability of nonsmooth one-variable functions." In 2017 Constructive Nonsmooth Analysis and Related Topics (dedicated to the memory of V.F. Demyanov) (CNSA). IEEE, 2017. http://dx.doi.org/10.1109/cnsa.2017.7973965.

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Korolev, Vladimir, and Viktor Novoselov. "Stochastic model of the universe matter." In 2017 Constructive Nonsmooth Analysis and Related Topics (CNSA). IEEE, 2017. http://dx.doi.org/10.1109/cnsa.2017.7973974.

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Mezentsev, Yurii, and Igor Estraykh. "Problems and optimization algorithms of schedules of parallel-serial systems with undefined service routes." In 2017 Constructive Nonsmooth Analysis and Related Topics (CNSA). IEEE, 2017. http://dx.doi.org/10.1109/cnsa.2017.7973988.

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Baran, Inna, and Igor Orlov. "Adjoint extremal problem for non-smooth functionals." In 2017 Constructive Nonsmooth Analysis and Related Topics (CNSA). IEEE, 2017. http://dx.doi.org/10.1109/cnsa.2017.7973933.

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9

Chernousko, Felix. "Dynamics of a body with internal moving masses in the presence of dry friction." In 2017 Constructive Nonsmooth Analysis and Related Topics (CNSA). IEEE, 2017. http://dx.doi.org/10.1109/cnsa.2017.7973948.

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Erokhin, Vladimir. "A stable solution of linear programming problems with the approximate matrix of coefficients." In 2017 Constructive Nonsmooth Analysis and Related Topics (CNSA). IEEE, 2017. http://dx.doi.org/10.1109/cnsa.2017.7973953.

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