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Mathematics
Optimizational approach to solving queries of complex systems synthesis is in itself a big reserve for elevating quality of econometrics, planning, management and projecting. The choice of optimizational aim areas of changing parameters is the task of particular economic and technical brunches of science.
Using my method I successfully solved test queries given by Wolf, H.H.Rosenbrock and J.D. Powell, as well as different sets of non-linear equations. My universal method of finding optimal solution for the above-enumerated programming queries consist of two well-known and simple algorithms: method of proportionally deformed polyhedron and method of gradient descending. It is well known that these two methods usually produce only local, separate solutions. But it is not true for my technique. In the algorithm these simple methods let me always acquire global solutions. Obviously there is no magic in it. The results obtained by me (proved theoretically) are the effects of extending the theory of convex functions. My algorithm was checked during two years of investigations and illustrated by solving of several hundred, better to say thousand of, tests and real nonlinear equations (from 1 up to 12500), differential equation (not all of them were included in this work as examples) and also applied theoretically.
EXAMPLES.
1. Multiple-extreme goal functions and non-convex and non-linked zones.
Minimize EE1=0.001((X1-10)(X1-1)(X1-2)(X1-3)(X1-4)(X1-5)(X1-6)(X1-7)(X1-8(X1-9)+COS(17X1)(X2-5)(X2-6). Where : EE2=(SIN(X1+X2))2 0. Solution: EE1=-42.934, X1=1.292, X2=11.279, EE2=0.000.
2. Let Y - a function-decision of differential equation, Y1,Y2,Y3 -first, second, third derived, T - an argument. To solution differential equation F=EXP (-ABS(Y**2+SIN(Y)+ Y1**3-EXP(-ABS(Y-Y1+SIN(T)-COS(T)))))-T*Y*Y1**3=0 on the interval of integrating [0 - 5], with the step of integrating 0.500. Solution: Total mistake is 0.0001. Number of iterations = 5. Function-decision of differential equation:Y=-.17001*SIN(.27549*T) +.45688*SIN(.13716*T)+-.10375*SIN(.25196*T)+.40123*COS(.29190*T)+ 10*-.79475*COS(.03287*T)+5*-.02601*COS(.52977*T)+0.1*.77562* EXP(-.12054*T)+0.01*-.12152*EXP(-.19184*T)+0.001*.38938*EXP(-.05314*T)+-.26027.
3. Where : T(1), T(2)-arguments, Y- function-solution, Y1(1)=Y/[T(1)], Y1(2)=Y/[T(2)], Y2(1,2)=Y/[T(1) T(2)]. To solution differential equation in private derived (ABS(COS(Y*T(1)*T(2))+Y1(1)+Y1(2)+Y-T(2)*Y2(1,1))) **(5-COS(-11*T(1)*T(2)*Y2(1,2)*Y*COS(T(1)*SIN(Y1(1)*Y1(2)*T(1)) *T(2)*Y2(1,2)*Y2(2,1))))+Y*T(1)*T(2)*Y2(1,2)*Y1(2)=0 on the interval of integrating [0 - 1], with the step of integrating 0.200.
Solution. Maximum mistake = 0.002. Total mistake = 0.026. Function-solution of differential equation: Y=0.41004*SIN(0.07469*T(1)+0.14477*T(2))+0.15094
Note. Abstracts are published in author's edition
Last update: 06-Jul-2012 (11:52:45)