By M.I. Zelikin, S.A. Vakhrameev

ISBN-10: 3642086039

ISBN-13: 9783642086038

The single monograph at the subject, this e-book issues geometric equipment within the concept of differential equations with quadratic right-hand aspects, heavily relating to the calculus of adaptations and optimum regulate concept. in response to the author’s lectures, the ebook is addressed to undergraduate and graduate scholars, and medical researchers.

**Read or Download Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations (Encyclopaedia of Mathematical Sciences) PDF**

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This complaints quantity incorporates a number of papers provided on the 3rd overseas convention on excessive functionality clinical Computing held on the Hanoi Institute of arithmetic, Vietnamese Academy of technological know-how and know-how (VAST), March 6-10, 2006. The convention has been prepared by means of the Hanoi Institute of arithmetic, Interdisciplinary middle for clinical Computing (IWR), Heidelberg, and its foreign PhD software "Complex methods: Modeling, Simulation and Optimization'', and Ho Chi Minh urban collage of expertise.

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**Additional info for Control Theory and Optimization I: Homogeneous Spaces and the Riccati Equation in the Calculus of Variations (Encyclopaedia of Mathematical Sciences) **

**Example text**

Kortanek. Semi-infinite programming: Theory, methods and applications, SIAM Review, 35:380-429, 1993. [39] R. B. Holmes. Geometric Functional Analysis and its Applications. SpringerVerlag, New-York, 1975. [40] R. G. Jeroslow and K. O. Kortanek. On semi-infinite systems of linear inequalities. Israel J. , 10:252-8, 1971. [41] H. Th. -J. Riickmann, and G. W. Weber. One-parametric semi-infinite optimization: on the stability of the feasible set. SIAM J. , 4:637-48,1994. [42] H. Th. Jongen, F. Twilt, and G.

It can be shown that there exists a local CDO -coordinate transformation, sending x onto the origin, such that M locally takes the following form: {x E IR n I TJkeO ~ 0, e = 1, ... ,p}, 'l/it where TJke equals ('l/i~e) if Ye is an interior point (boundary point) and where the argument of TJkl is the first k1 -block of coordinates Xl, ... , Xk l , the argument of TJk2 is the next k 2 -block of coordinates Xk l +1, ... , Xk l +k 2, etc. In case that the Reduction Ansatz is applicable, we have ke = 1, e = 1, ...

De ABSTRACT In this tutorial paper we study finite dimensional optimization problems with infinitely many inequality constraints. We discuss the structure and stability of the feasible set, as well as stability of stationary points. Then, we consider global (or structural) stability of semi-infinite optimization problems and, finally, we focus on one-parametric deformations of them. 2) Y = {y E lRT I Ui(Y) = 0, i E I, Vj(Y) 2:: 0, j E J}, M[h,gj = -h = (hi, i E A), IAI < n, III < r, IJI < 00 (where I· I denotes the cardinality).

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