II Semester M.E. (Power & Energy Systems) Degree Examination, January 2013 2K8 PS 211 : LINEAR & NON-LINEAR OPTIMIZATION Time : 3 Hours
Max. Marks : 100
Instruction: Answer any five full questions. 1. a) What are the characteristics of constrained optimization problems ? Briefly explain.
8
b) A person has to provide 10, 12 and 12 units of chemicals A, B and C respectively to his Garden. A liquid product contains 5, 2 and 1 units of chemical A, B and C respectively per Jar and costs ` 3/- per Jar. A dry product contains 1, 2 and 4 units of chemical A, B and C respectively per packet and costs ` 2/- per packet. How many of these the person should purchase to meet the requirements at least cost ? Formulate as an LPP and solve graphically. 12 2. a) With reference to the solution of LPP by Simplex method/table when do you conclude as follows i) LPP has multiple optimum solutions ii) LPP has no limit for improvement of the objective function. iii) LPP has no feasible solution. b) What are the properties of duality ?
6 4
c) Use K-T conditions to solve the Non-Linear Programming problems Maximize z = 7 x12 − 6 x1 + 5 x 22 Subject to x1 + 2x 2 ≤ 10 x1 – 3x2 ≤ 9 x1, x2 ≥ 0.
10
3. a) Explain the procedure of solving an LPP by Dual Simplex Method.
6
b) State the optimal control problem. Derive the necessary conditions for optimal control.
6
c) Find the minimum of f = λ5 − 5 λ3 − 20 λ + 5 using Quadratic Interpolation Method.
8 P.T.O.
*EJM011*
EJM – 011 4. a) Use Lagrangian multiplier to solve Min Z = x12 + x 22 + x 23 . Subject to x1 + 2x2 + x3 = 4 x1 + x2 + x3 = 3. b) Define Unimodal and multimodal functions.
6 4
c) Solve the following LPP using Revised Simplex Method : Minimize Z = 3x1 + x2 + x 3 + x4 Subject to – 2x1 + 2x2 + x3 = 4 3x1 + x2 + x4 = 6 x1 ≥ 0, x2 ≥ 0, x3 ≥ 0 and x4 ≥ 0. 5. a) Explain the following methods with the help of flow-chart. i) Powell’s method ii) Steepest Descent Method.
10
10
b) Maximize f( x) = x 12 + 3 x 22 + 6 x 23 by univariate method starting from (2 –1 1). Obtain the value of the function after two iterations. 10 6. a) Explain Economic Dispatch by Gradient Method.
6
b) Explain in brief the Genetic Algorithm Operators.
6
c) How are the search directions generated in Fletcher-Reeves Method ? Explain with an example.
8
7. a) Explain the optimization of Fuzzy Systems. b) Explain optimal power flow based on Newton Method.
6 6
c) Use Hooke and Jeeve’s method to minimize the function f (x1 x 2 ) = x12 + 3x22 by taking Δx 1 = Δx 2 = 0 .5 starting from (2, –1). Obtain the value of f(x) after two iterations. ______________
x1 ⥠0, x2 ⥠0, x3 ⥠0 and x4 ⥠0. 10. 5. a) Explain the following methods with the help of flow-chart. i) Powell's method. ii) Steepest Descent Method. 10.
Apr 11, 2008 - iss = 1 β while in the steady-state, all the adjustment should cancel out so that xss = yss yflex,ss. = 1 (no deviations from potential/flexible output level, yflex,ss). The log-linearization assumption behind the Phillips curve is th
High resolution mass spectra (HRMS) were ... fication (CPA) system comprising of an oscillator (Maitai, .... HRMS (m/z): [M + Na] calcd for C19H16N2O5Na;.
... the apps below to open or edit this item. pdf-1450\linear-and-nonlinear-programming-internatio ... ns-research-management-science-3rd-third-edition.pdf.
where α is the matrix of functions of B, a is the column vector of solution parameters ..... example is trivialâespecially knowing that the analytic solution is easily ...
Sometimes all state space variables are not available for measurements, or it is not practical to measure all of them, or it is too expensive to measure all state space variables. In order to be able to apply the state feedback control to a system, a
become more pertinent in light of the large amounts of data that we ...... Along with the development of richer representation structures, recently there has.
Aug 5, 2004 - H. - _- o 0o0. 2 1 ..|4. 03:5'. 6 0. o a. Mn. 0m 8. Me. 0m T. n n b. 50 1| - 4.I. FIG. 26. FIG. 1C .... The seismic waves are detected at or near the surface by seismic receivers. .... 13 illustrates a shift register of degree 4 With fe
and x1 x2 x3 ⥠0. 10. 5. a) What is a unimodal function ? What is the difference between Newton and. Quasi Newton methods ? 6. b) Explain univariate method.
Reactive planners improvise solutions at run time as uncertainties, predicted or unpredicted, arise. A conditional plan does not exhibit the 'persistent goal- ..... 4) The contexts for the goals in the plan form a tautol- ogy. The context of every po
system theory is not much beyond the typical third- or fourth-year undergraduate course ... Use of this material for business or commercial purposes is prohibited. .... A system represented by (5) will be called a degree-n homogeneous system.
noisy speech, these two operations lead to some degrada- tion in recognition performance for clean speech. In this paper, we try to alleviate this problem, first by introducing the energy information back into the PAC based features, and second by st
Use inequalities to model and solve real-life problems. *We have discussed ... Ex) Solve the following polynomial inequality and show on the x â axis which x â values are in the solution. set. 3 2 2 3 32 48 xx x â â >â. TURN OVER. Page 3 of
in many machine learning areas where essentially low-dimensional data is nonlinearly ... low dimensional representation of xi. ..... We explain this in detail.
