35,690 research outputs found
On the metric regularity of affine optimal control problems
No full textThe paper establishes properties of the type of (strong) metric regularity of the set-valued map associated with the system of necessary optimality conditions for optimal control problems that are affine with respect to the control (shortly, affine problems). It is shown that for such problems it is reasonable to extend the standard notions of metric regularity by involving two metrics in the image space of the map. This is done by introducing (following an earlier paper by the first and the third named author) the concept of (strong) bi-metric regularity in a general space setting. Lyusternik-Graves-type theorems are proved for (strongly) bi-metrically regular maps, which claim stability of these regularity properties with respect to “appropriately small” perturbations. Based on that, it is proved that in the case of a map associated with affine optimal control problems, the strong bi-metric regularity is invariant with respect to linearization. This result is complemented with a sufficient condition for strong bi-metric regularity for linear-quadratic affine optimal control problems, which applies to the “linearization” of a nonlinear affine problem. Thus the same conditions are also sufficient for strong bi-metric regularity in the nonlinear affine problem
Higher-order numerical scheme for linear quadratic problems with bang–bang controls
Full text linkThis paper considers a linear-quadratic optimal control problem where the control function appears linearly and takes values in a hypercube. It is assumed that the optimal controls are of purely bang-bang type and that the switching function, associated with the problem, exhibits a suitable growth around its zeros. The authors introduce a scheme for the discretization of the problem that doubles the rate of convergence of the Euler's scheme. The proof of the accuracy estimate employs some recently obtained results concerning the stability of the optimal solutions with respect to disturbances
Gradient methods on strongly convex feasible sets and optimal control of affine systems
No full textThe paper presents new results about convergence of the gradient projection and the conditional gradient methods for abstract minimization problems on strongly convex sets. In particular, linear convergence is proved, although the objective functional does not need to be convex. Such problems arise, in particular, when a recently developed discretization technique is applied to optimal control problems which are affine with respect to the control. This discretization technique has the advantage to provide higher accuracy of discretization (compared with the known discretization schemes) and involves strongly convex constraints and possibly non-convex objective functional. The applicability of the abstract results is proved in the case of linear-quadratic affine optimal control problems. A numerical example is given, confirming the theoretical findings
Metric Regularity Properties in Bang-Bang Type Linear-Quadratic Optimal Control Problems
Full text linkThe paper investigates the Lipschitz/Hölder stability with respect to perturbations of the solutions of linear-quadratic optimal control problems where the control variable appears linearly and the optimal one is of bang-bang type. Conditions for bi-metric regularity and (Hölder) metric sub-regularity are established, involving only the order of the zeros of the associated switching function and smoothness of the data. The results provide a basis for investigation of various approximation methods and are applied in this paper for convergence analysis of a Newton-type method
On the Regularity of Linear-Quadratic Optimal Control Problems with Bang-Bang Solutions
No full textThe paper investigates the stability of the solutions of linear-
quadratic optimal control problems with bang-bang controls in terms of
metric sub-regularity and bi-metric regularity. New sufficient conditions for these properties are obtained, which strengthen the known conditions for sub-regularity and extend the known conditions for bi-metric regularity to Bolza-type problems
Keeping a learned society young
Full text linkAging organizations - regardless of whether they are firms, faculties, societies, political bodies, teams, or national academies - seek ways to rejuvenate. This paper demonstrates that the best way to keep an organization young is through a mixed strategy of recruiting both young and old, and that, contrary to intuition, recruiting those of middle age is the least effective strategy for maintaining a younger age structure. The aging of learned societies is a problem in many national academies. Faced with rising life expectancy, particularly for older persons, the average age of academy members is increasing. Another reason for "overaging" is an increase in the age at election. In an organization with a fixed size, the annual intake is strictly determined by the number of deaths and the statutory retirement age. This can, among many learned societies, lead to a fundamental dilemma: the desire to maintain a young age structure, while still guaranteeing a high recruitment rate. We derive an optimal recruitment policy which is bimodal, i.e., it entails shifting recruitment partly to younger ages and partly to older ages, while decreasing the recruitment of middle-aged candidates. Although the optimization problem explicitly involves only the average age and the recruitment rate as objectives, the methodology implicitly allows us to take into consideration all other objectives (formal or informal) used in the actual election practice.age-specific recruitment policy, fixed-size population, optimal control
Informetrics on M. N. Srinivas
Full text linkM. N. Srinivas, the well known sociologist is widely recognised as architect of modern Indian sociology and social anthropology. His publications have been analysed by year, domain, authorship pattern, channels of communication used. Keywords, etc. The results indicate that the papers published by him are of a nature that qualify him to be a 'role model' for the younger generations to emulate.
By the end of 1995, Srinivas had to his credit 144 papers which, included 33 broad papers in sociology and anthropology; 18 papers in social change; 28 papers in village studies; 12 papers on religion; 17 papers on caste and 36 papers of general popular interest. The periods 1958-61 and 1974-77, when Srinivas was 38-41 and 58-61 years old. were his most productive periods with highest publication activity
Climate Change and Technical Progress: Impact of Informational Constraints
Full text linkBondarev A, Clemens C, Greiner A. Climate Change and Technical Progress: Impact of Informational Constraints. Working Papers in Economics and Management. Vol 01-2013. Bielefeld: Bielefeld University, Department of Business Administration and Economics; 2013.In this paper we analyse a growth model that includes environmental and economic variables as well as technological progress under different informational constraints on the behavior of economic agents. To simulate the informationally constrained economy, we make use of the non-linear model predictive control technique. We compare models with exogenous and endogenous technical change as well as directed and undirected endogenous technical change under different informational structures. We show that endogenous technical change yields lower environmental damages than exogenous technical change with fully informed agents. At the same time, welfare may rise or decline depending on the efficiency of the technology in use. In the case of directed technical change, a green growth scenario generates a smaller temperature increase that, however, goes along with less output and lower welfare. This holds both for informationally constrained and unconstrained behaviour of agents. We find that the effects of informational constraints, with respect to the climate system, increase with the degree of endogeneity of technology in the model
Illuminaçao Apologetica do retrato de Morteçor en que aparecem com mais vivas côres os erros do author do novo Methodo, e seu Apologista ...
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From the correspondence of M. P. Drahomanov: two unknown letters to M. V. Vodovozov of 1894
No full textThis publication introduces into scientific discourse little-known letters of prominent Ukrainian scholar, politician and publicist M. P. Drahomanov (1841-1895), discovered in the fond of V. I. Vernadsky in the Archive of the Russian Academy of Sciences in Moscow. Two letters written in the latest period of the life of M. P. Drahomanov, which are addressed to young economist and publicist Mykola Vasyliovych Vodovozov (1870-1896), expand the source base not only for M. P. Drahomanov’s biographers. They show his ties with Russian liberals, who later formed the core of the party of constitutional democrats. A preface to the publication contains a biography of M. V. Vodovozov, and the author makes a hypothesis on the history of an acquaintance of the correspondent and the addressee, which could be connected with M. V. Vodovozov’s brother, V. V. Vodovozov, and members of the “Shelter Fraternity”, and through them with M. P. Drahomanov. The analysis of the published letters proves that M. P. Drahomanov endeavored to widen through the “Shelter Fraternity” members his contacts with democratic circles in Russia, and also to find financial support for publishing letters of Bakunin and Struve
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