What is Minimization: Definition and 96 Discussions

In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorithms accomplishing this task are known and described in standard textbooks on automata theory.

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  1. chwala

    Find the dimensions that will minimize the surface area of a Rectangle

    My interest is on number 11. In my approach; ##v= xyz## ##1000=xyz## ##z= \dfrac{1000}{xy}## Surface area: ##f(x,y)= 2( xy+yz+xz)## ##f(x,y)= 2\left( xy+\dfrac{1000}{x} + \dfrac{1000}{y}\right)## ##f_{x} = 2y -\dfrac{2000}{x^2} = 0##...
  2. F

    I Optimization problem with multiple outputs: impossible?

    Hello, I'm facing a practical optimization problem for which I don't know whether a standard approach exists or not. I would have liked to rephrase the problem in a more general way, for the sake of "good math", but I'm afraid I would leave out some details that might be relevant. So, I'm going...
  3. gratusri

    Optimizing and minimization of a Deterministic Finite Automata

    so this is the question , I have to minimize this DFA this is How I did it but when I checked for answers , this is what it was, can someone please explain to me what mistake I made? I have been wondering about this for past 2 days
  4. Simobartz

    I Minimization of thermodynamic equilibrium

    Hi, I don't understand what does it mean that at equilibrium the proper thermodynamic potential of the system is minimized. For example on the book Herbert B. Callen - Thermodynamics and an Introduction to Thermostatistics it is written: Helmholtz Potential Minimum Principle. The equilibrium...
  5. M

    Optimization: Dual for L1 norm minimization with equality constraint

    Hi, I was reading through some notes on standard problems and their corresponding dual problems. I came across the L2 norm minimization for an equality constraint, and then I thought how one might formulate the dual problem if we had an L1-norm instead. Question: Consider the following...
  6. Leo Liu

    Minimization problem using partial derivatives

    a) ONLY The common way to solve this problem is minimizing the two-variable equation after using the substitution ##z^2=1/(xy)##. Yet I wondered if it is possible to optimize the distance equation with three varibles. So I wrote the following equations: Distance: $$f(x,y,z)=s^2=x^2+y^2+z^2$$...
  7. B

    Python Minimization likelihood function with parameters

    Hallo at all! I'm learning statistic in python and I have a problem to show you. I have this parametric function: $$P(S|t, \gamma, \beta)=\langle s(t) \rangle \left( \frac{\gamma-\beta}{\gamma\langle s(t) \rangle -\beta}\right)^2\left( 1- \frac{\gamma-\beta}{\gamma\langle s(t) \rangle...
  8. anemone

    MHB Real Roots of Polynomial Minimization Problem

    For an integer $n\ge 2$, find all real numbers $x$ for which the polynomial $f(x)=(x-1)^4+(x-2)^4+\cdots+(x-n)^4$ takes its minimum value.
  9. P

    I Minimization of free energy in Landau theory

    Thanks in advance for any insight! Following Pathria's discussion of phase transitions, I'm getting tripped up on the discussion of Landau's theory. Pathria begins with a zero-field free energy ##\psi = A/NkT## where ##A## is the Helmholtz free energy. He proceeds to characterize the...
  10. M

    Solving the Minimization Operator Problem

    Homework Statement Given a Hilbert space $$V = \left\{ f\in L_2[0,1] | \int_0^1 f(x)\, dx = 0\right\},B(f,g) = \langle f,g\rangle,l(f) = \int_0^1 x f(x) \, dx$$ find the minimum of $$B(u,u)+2l(u)$$. Homework Equations In my text I found a variational theorem stating this minimization problem...
  11. K

    Minimization problem: Economics: quantity to order

    Homework Statement Homework Equations Minimum/Maximum occurs when the first derivative=0 The Attempt at a Solution $$Q=\sqrt{\frac{2(K+pQ)}{h}}~\rightarrow~Q=\frac{2}{h}(KM+pM)$$ ##Q'=0~## gives no sense result
  12. T

    Difference between Energy Minimization and Equilibration

    What is the exact difference between energy minimization and equilibration in a molecular dynamics simulation since both brings the system to the local energy minima?
  13. T

    I Minimization using Lagrange multipliers

    Given the following expressions: and that ## \bf{B}_s = \nabla \times \bf{A}_s ## how does one solve for the following expressions given in (12) and (13)? I've attempted doing so and derive the following expressions (where the hat indicates a unit vector): ## bV = \bf{ \hat{V}} \cdot...
  14. T

    Minimization of a paper cup

    Homework Statement company manufactures paper cups that are designed to hold 8 fluid ounces each. The cups are in the shape of a frustum of a right circular cone (so the top and bottom of the cup are circles, not necessarily of the same size, and the side profile is that of a...
  15. J

    Cryptographic attacks as minimization of degree 4 polynomial

    Cryptography is based on reason-result chains like hash functions: which are inexpensive to propagate in the intended direction, but seem hard to reverse. However, decomposing them into satisfaction of simple (direction-agnostic) relations like 3-SAT clauses, may bring a danger of existence of...
  16. V

    MHB What is the strategy for solving Problem S395 in Mathematical Reflections?

    If $a^2b^2+b^2c^2+c^2a^2-69abc=2016$, then, what can be said about the least value of $\min(a, b ,c)$? This problem is unyielding to the major inequalities like AM-GM, Cauchy-Schwarz, etc. I also tried relating it to $x^3+y^3+z^3-3xyz=(x+y+z)(\sum_{cyc}x^2+\sum_{cyc}xy)$, but of no use. Any...
  17. E

    MATLAB Plotting graph 3D minimization

    Hi to everyone, I'm trying to plot a 3D graph on MATLAB but I do not know how. The function that I want to plot is: y=fminbnd(@(x) wei(x,shape,scale,tw,tf),x0,x1). I would like to plot the minimization of the function wei (y) in function of the shape and the scale. Wei is a function that I...
  18. I

    Weber-Fermat Problem, degenerate cases

    Homework Statement I have to prove some things on the Weber-Ferma problem. Here is the assignment : We want to find a point $$x$$ in the plane whose sum of weighted distances from a given set of fixed points $$y_1, ...,y_m$$ is minimized. 1-Show that there exist a global mimimum to the...
  19. N

    A Certain convex minimization problem

    Hi, I would like to know if the inequality sign plays any role to the following optimization problem: minimize f0(x) subject to f1(x)>=0 where both f0(x) and f1(x) are convex. The standard form of these problems require a constraint such as: f1(x)<=0, but i am interested in the opposite...
  20. K

    Minimization of objective function

    Hi, I need to minimize, with respect to \hat{y}(x), the following function: \tilde{J}_x = \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)^2] + \nu \mathbb{E}_{p(x,y)}[(\hat{y}(x)-y)tr(\nabla_x^2\hat{y}(x))] + \nu \mathbb{E}_{p(x,y)}[||\nabla_x\hat{y}(x)||^2], where x is a vector and y a scalar. I found this...
  21. patrickbotros

    A Find the minimum without Calculus or Graphing

    ƒ(ß)=.5sec(ß) + √[1+(sec2(ß)/4)+tan(ß)/√(2)] Without graphing it or using calculus find the minimum. I already know the answer but want to know how to do it. It s at π/12 and is something like 1.5. First off this is NOT a homework problem. I already know the answer is something like 1.5 at π/12...
  22. S

    Minimizing surface area of a shaker

    Hi, I have an mathematics assignment to do, and I wonder if the topic I have chosen is doable for me. I want to minimize the surface area of a cobbler cocktail shaker, and until now my plan was to get the curve equation for the side of it, and get the area equation from surface of revolution...
  23. Paul I.

    Minimizing Illumination with Two Light Sources on a Parallel Line

    Homework Statement Two light sources of identical strength are placed 8 m apart. An object is to be placed at a point P on a line ℓ parallel to the line joining the light sources and at a distance d meters from it (see the figure). We want to locate P on ℓ so that the intensity of illumination...
  24. G

    Minimization of many-variable function

    Hi, I'm learning python and I'm just trying to minimize a function of many variables, but I have some problems with my code. import numpy as np import scipy.optimize as op from scipy.optimize import minimize table1_np = np.genfromtxt('Data/tabla1.txt', usecols=0) #--------------------------...
  25. D

    GSL Multidim Minimizer - How to handle unphyiscal values

    Hello, For my master thesis I'm looking at the Two-Higgs-Doublet-Modell at finite Temperature and I'm searching for the Minimum values of the two VEVs of the Doublets. Therefore i have my Potential with Input Parameters v1 and v2 in which I want to minimize the Potential and a Vector with User...
  26. N

    Graphical meaning of tangent in optimization problem

    In a trivial optimization problem, when seeking the value of x2 that minimizes y(x2)/(x2-x1), the solution is graphically given by the tangent line shown in the figure. I'm having a lot of difficulty understanding why this is true, i.e., the logical steps behind the equivalence supporting the...
  27. B

    Binary classification: error probability minimization

    Typically in problems involving binary classification (i.e. radar detection, medical testing), one will try to find a binary classification scheme that minimizes the total probability of error. For example, consider a radar detection system where a signal is corrupted with noise, so that if the...
  28. kostoglotov

    Part Derivs: Minimizing the Weight of a Rocket

    Homework Statement This is actually an Applied Project in the text, and overall is quite a large problem, so I won't post the entire thing, as there are lots of equations and steps where the text guides me by saying "show that...this thing...then...show that this other thing..." What I need...
  29. I

    MHB Relation within Gauss-Newton method for minimization

    If we study model fit on a nonlinear regression model $Y_i=f(z_i,\theta)+\epsilon_i$, $i=1,...,n$, and in the Gauss-Newton method, the update on the parameter $\theta$ from step $t$ to $t+1$ is to minimize the sum of squares...
  30. D

    Minimization with cos()^2

    I'm trying to find a increasing postive function \phi (x) that minimizes the following integral for x in [0, L]: \int_0^L A \frac{ d ^2 \phi (x) } {dx^2}+ (B +C cos( \phi (x)) ^2 \mbox{d}x with A and B real positve numbers and \phi (0) =0 \phi ' (L) =0 When I use the the Lagrange...
  31. D

    Minimizing Aphi' + Bcos(phi) in [0,L] w/ phi(0)=0

    I'm trying to find a function for x in [0, L] that minimizes this: \int_0^{L} A \phi(x) \frac{ d \phi(x) }{dx} + B cos(\phi(x))\ d\mbox{x} For real (given) positve numbers A and B. with \phi(0) = 0 \phi(x) is an increasing positve function. Can somebody point me in the right direction?
  32. K

    How do I determine shaded cells in K-tables for minimizing multiple outputs?

    Homework Statement http://i.imgur.com/VYPECuW.png?1 (f1: f2: f3: f1*f2: f1*f3: f2*f3: f1*f2*f3: is what's written near tables) I need to minimize the functions (sum of minterms: f1 0, 1, 2, 4, 5, 11, 15; f2 0, 2, 4, 13, 15; f3 0, 1, 3, 4, 5, 7, 13, 15) using K-tables... This is what they show...
  33. T

    Law of the minimization of mystery

    Several theories try and explain consciousness from a quantum perspective. Most notoriously the Penrose-Hameroff Orch OR hypothesis comes to mind, but there are others by Henry Stapp, Giuseppi Vitiello, and Gustav Bernroider to name a few. The consciousness philosopher David Chalmers has...
  34. R

    Iterative Minimization lemma proof

    Homework Statement f(x) is the function we want to minimize. Beyond being real-valued, there are no other conditions on it. (I'm surprised it's not at least continuous, but the book doesn't say that's a condition.) We choose the next x^k through the relation x^k = x^{k-1} + \alpha_{k}d^k. We...
  35. R

    Optimization problem: minimization

    Homework Statement Minimize the function f(x,y) = \sqrt{x^2 + y^2} subject to x + y \leq 0. Show that the function MP(z) is not differentiable at z = 0. Homework EquationsThe Attempt at a Solution I haven't gotten anywhere because I don't understand why the solution isn't trivial, i.e. (0,0)...
  36. S

    Gnuplot: x squared minimization method

    Hello, I am using the x squared minimization method to compute two parametres in a function let's say (A,B) which correspondes to the minimum value of x^2. Now if i want to make a contour plot of A,B (A=x axis and B=y axis) for the values of x^2-x^2_(minimum)=1σ=2.3 what is the proper way...
  37. S

    MHB How is the Retail Price Calculated with a 40% Markup?

    Can someone also check this one on my answers. Again, it's just a homework assignment. Thanks for your help.
  38. S

    MHB Check My SOP Minimization Circuit: Homework Help

    Can someone check my work and make sure I drew the circuit correctly? This is just a homework assignment. Thanks in advance.
  39. D

    Fortran Numerical Minimization of many-variable function in Fortran

    I would like to find a FORTRAN subroutine or a good way to minimize function numerically.So basically my function has 20 variables and I am able to provide analytic form of the first and the second derivative of the function. Basically what I want is: have the form of the function of 20...
  40. MarkFL

    MHB Minimize Sum of Line Segments Length w/ Point P on Line AD - Yahoo Answers

    Here is the question: I have posted a link there to this thread so the OP can see my work.
  41. S

    MHB Product of Sums Minimization KMap (Problem #2)

    Write out the minimal Product of Sums (POS) equation with the following Karnaugh Map. Just need someone to check my work please. I am questioning my self on my grouping. Did I group correctly or should I have grouped the bottom left 0 and D versus the 0 in the group of 8? Thanks for your time...
  42. binbagsss

    Inner product space - minimization.

    The question is : If the vector space C[1,1] of continuous real valued functions on the interval [1,1] is equipped with the inner product defined by (f,g)=^{1}_{-1} \intf(x)g(x)dx Find the linear polynomial g(t) nearest to f(t) = e^t? So I understand the solution will be given by...
  43. M

    MATLAB Why is MATLAB giving me a wrong answer when solving a minimization problem?

    In MATLAB, I am using fmincon to solve a minimization problem with nonlinear constraints. The problem is that, it is giving me a wrong answer, a point that is not a minimizer (not even close), and that is not within the tolerance. I made sure to use a feasible initial point. However, when I...
  44. G

    Matrix trace minimization and zeros

    Hello, :) I would like to minimize and find the zeros of the function F(S,P)=trace(S-SP’(A+ PSP’)^-1PS) in respect to S and P. S is symmetric square matrix. P is a rectangular matrix Could you help me? Thank you very much All the best GoodSpirit
  45. P

    Optimizing Total Cost: Finding MTBF for Maximum Savings in 5 Years

    Homework Statement A system is to be operated 5000 hours per year, where Total Cost (for 5 years) = Acquisition cost + Spares cost + Downtime cost System acquisition cost is related to MTBF, θ, as follows: CA(θ) = 685.2917e0.003779θ The average cost of a spare item is $1,000 and the...
  46. T

    Simplex minimization problem reformation with modulus cost function

    Homework Statement If I said minimize the cost function |a-2b| + |-3a-b| subject to 2a + b <= 6 a,b >= 0 We can all see it's 0,0 but if I want to apply the simplex algorithm to it, how do I reformulate the problem into something I can use Homework Equations The Attempt at...
  47. C

    Explanation on minimization of Expected values

    Why is the E[ Y - f(x) ]^2 minimized when choosing f(x) = E[Y|X] ?
  48. D

    Solve Area Minimization Question: Tent w/o Bottom & Triangles

    I've got a question that I don't know how to solve. The question is: We want to produce a tent, without a bottom part, which has two rectangular sides and two gables in the form of two isosceles triangles with the base against the ground. Determine the height of the tent, which has volyme V and...
  49. B

    Classical Mechanics: Minimization of geodesic on a sphere

    Homework Statement Use the result (6.41) of Problem 6.1 to prove that the geodesic (shortest path) between two given points on a sphere is a great circle. [Hint: The integrand f(ψ,ψ',θ) in (6.41) is independent of ψ, so the Euler-Lagrange equation reduces to ∂f/ψ' = c, a constant. This gives...