DSpace Collection: Volume 39, Number 3-4
http://hdl.handle.net/10525/2816
Serdica Mathematical Journal Volume 39, Number 3-4, 2013The Collection's search engineSearch the Channelsearch
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Viability and an Olech Type Result
http://hdl.handle.net/10525/3447
Title: Viability and an Olech Type Result<br/><br/>Authors: Krastanov, M. I.; Ribarska, N. K.<br/><br/>Abstract: 2010 Mathematics Subject Classification: 34A36, 34A60.<br/><br/>Description: [Krastanov M. I.; Кръстанов М. И.]; [Ribarska N. K.; Рибарска Н. К.]Regularity of Set-Valued Maps and Their Selections through Set Differences. Part 2: One-Sided Lipschitz Properties
http://hdl.handle.net/10525/3446
Title: Regularity of Set-Valued Maps and Their Selections through Set Differences. Part 2: One-Sided Lipschitz Properties<br/><br/>Authors: Baier, Robert; Farkhi, Elza<br/><br/>Abstract: We introduce one-sided Lipschitz (OSL) conditions of setvalued maps with respect to given set differences. The existence of selections of such maps that pass through any point of their graphs and inherit uniformly their OSL constants is studied. We show that the OSL property of a convex-valued set-valued map with respect to the Demyanov difference with a given constant is characterized by the same property of the generalized Steiner selections. We prove that an univariate OSL map with compact images in R^1 has OSL selections with the same OSL constant. For such a multifunction which is OSL with respect to the metric difference, one-sided Lipschitz metric selections exist through every point of its graph with the same OSL constant. 2010 Mathematics Subject Classification: 47H06, 54C65, 47H04, 54C60, 26E25.Regularity of Set-Valued Maps and their Selections through Set Differences. Part 1: Lipschitz Continuity
http://hdl.handle.net/10525/3445
Title: Regularity of Set-Valued Maps and their Selections through Set Differences. Part 1: Lipschitz Continuity<br/><br/>Authors: Baier, Robert; Farkhi, Elza<br/><br/>Abstract: We introduce Lipschitz continuity of set-valued maps with respect to a given set difference. The existence of Lipschitz selections that pass through any point of the graph of the map and inherit its Lipschitz constant is studied. We show that the Lipschitz property of the set-valued map withrespect to the Demyanov difference with a given constant is characterizedby the same property of its generalized Steiner selections. For a univariatemultifunction with only compact values in R^n, we characterize its Lipschitz continuity in the Hausdorff metric (with respect to the metric difference) by the same property of its metric selections with the same constant. 2010 Mathematics Subject Classification: 54C65, 54C60, 26E25.On Cluster Points of Alternating Projections
http://hdl.handle.net/10525/3444
Title: On Cluster Points of Alternating Projections<br/><br/>Authors: Bauschke, Heinz H.; Noll, Dominikus<br/><br/>Description: 2010 Mathematics Subject Classification: Primary 65K10; Secondary 47H04, 49M20, 49M37,65K05, 90C26, 90C30.On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics
http://hdl.handle.net/10525/3443
Title: On the Optimal Control of Some Parabolic Partial Differential Equations Arising in Economics<br/><br/>Authors: Boucekkine, R.; Camacho, C.; Fabbri, G.<br/><br/>Abstract: We review an emerging application field to parabolic partial differential equations (PDEs), that’s economic growth theory. After a short presentation of concrete applications, we highlight the peculiarities of optimal control problems of parabolic PDEs with infinite time horizons. In particular, the heuristic application of the maximum principle to the latter leads to single out a serious ill-posedness problem, which is, in our view, a barrier to the use of parabolic PDEs in economic growth studies as the latterare interested in long-run asymptotic solutions, thus requiring the solutionto infinite time horizon optimal control problems. Adapted dynamic programming methods are used to dig deeper into the identified ill-posedness issue. 2010 Mathematics Subject Classification: 91B62, 91B72, 49K20, 49L20.Recent Results on Douglas–Rachford Methods
http://hdl.handle.net/10525/3442
Title: Recent Results on Douglas–Rachford Methods<br/><br/>Authors: Artacho, Francisco J. Aragón; Borwein, Jonathan M.; Tam, Matthew K.<br/><br/>Abstract: Recent positive experiences applying convex feasibility algorithms of Douglas–Rachford type to highly combinatorial and far from convex problems are described. 2010 Mathematics Subject Classification: 90C27, 90C59, 47N10.About Uniform Regularity of Collections of Sets
http://hdl.handle.net/10525/3441
Title: About Uniform Regularity of Collections of Sets<br/><br/>Authors: Kruger, Alexander Y.; Thao, Nguyen H.<br/><br/>Abstract: We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving feasibility problems. 2010 Mathematics Subject Classification: 49J53, 41A25, 74S30.Newton-secant Method for Functions With Values in a Cone
http://hdl.handle.net/10525/3440
Title: Newton-secant Method for Functions With Values in a Cone<br/><br/>Authors: Pietrus, Alain; Jean-Alexis, Célia<br/><br/>Description: 2010 Mathematics Subject Classification: 49J53, 47H04, 65K10, 14P15.A Second-Order Maximum Principle in Optimal Control Under State Constraints
http://hdl.handle.net/10525/3439
Title: A Second-Order Maximum Principle in Optimal Control Under State Constraints<br/><br/>Authors: Frankowska, Hélène; Hoehener, Daniel; Tonon, Daniela<br/><br/>Abstract: A second-order variational inclusion for control systems under state constraints is derived and applied to investigate necessary optimality conditions for the Mayer optimal control problem. A new pointwise condition verified by the adjoint state of the maximum principle is obtained as well as a second-order necessary optimality condition in the integral form. Finally, a new sufficient condition for normality of the maximum principle is proposed. Some extensions to the Mayer optimization problem involving a differential inclusion under state constraints are also provided. 2010 Mathematics Subject Classification: 49K15, 49K21, 34A60, 34K35.Asymptotic Behavior in Sliding Mode Control Systems
http://hdl.handle.net/10525/3438
Title: Asymptotic Behavior in Sliding Mode Control Systems<br/><br/>Authors: Zolezzi, Tullio<br/><br/>Abstract: Practical stability of real states of nonlinear sliding mode control systems is related to asymptotic vanishing of the corresponding sliding errors. Conditions are found such that, if the equivalent control achieves exponential stability, then real states are practically stable. In special cases, their exponential stability is obtained. A link between convergence of regularization procedures and metric regularity is pointed out. 2010 Mathematics Subject Classification: 93B12, 93D15.Publications of Prof. Vladimir M. Veliov
http://hdl.handle.net/10525/3437
Title: Publications of Prof. Vladimir M. Veliov<br/><br/>Authors: Veliov, Vladimir M.<br/><br/>Description: [Veliov Vladimir M.; Вельов Владимир М.]Publications of Prof. Asen L. Dontchev
http://hdl.handle.net/10525/3436
Title: Publications of Prof. Asen L. Dontchev<br/><br/>Authors: Dontchev, Asen L.<br/><br/>Description: [Dontchev Asen L.; Дончев Асен Л.]Asen L. Dontchev (on the occasion of his 65th birthday) and Vladimir M. Veliov (on the occasion of his 60th birthday)
http://hdl.handle.net/10525/3435
Title: Asen L. Dontchev (on the occasion of his 65th birthday) and Vladimir M. Veliov (on the occasion of his 60th birthday)<br/><br/>Authors: Donchev, Tzanko; Krastanov, Mikhail; Ribarska, Nadezhda; Tsachev, Tsvetomir; Zlateva, Nadia<br/><br/>Description: [Donchev Tzanko; Дончев Цанко]; [Krastanov Mikhail; Кръстанов Михаил]; [Ribarska Nadezhda; Рибарска Надежда]; [Tsachev Tsvetomir; Цачев Цветомир]; [Zlateva Nadia; Златева Надя]