OPTIMIZATION.pptx

From the use of program by the united states military

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from the use of program by the United States military to refer to proposed training and logistics schedules, which were the problems Dantzig studied at that time.) Dantzig published the Simplex algorithm in 1947, and John von Neumann developed the theory of duality in the same year.
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OBJECTIVES The objectives of this presentation is to: 1. Maximize or minimize a real function 2. Solve an ordinary differential equation 3. Finding the absolute extrema 4. Determine the object’s parameters
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CONTINUOUS VS DISCRETE OPTIMIZATION There is a rather clear dividing line between discrete and continuous mathematics. Continuous mathematics is classical, well established, with a rich variety of applications. Discrete mathematics grew out of puzzles and then is often identified with specific application areas like computer science or operations research. Basic structures and methods of both sides of our science are quite different (continuous mathematicians use limits; discrete mathematicians use induction). This state of mathematics at this particular time, the turn of the millennium, is a product of strong intrinsic logic, but also of historical coincidence.
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CONTINUOUS VS DISCRETE OPTIMIZATION The main external source of mathematical problems is science, in particular physics. The traditional view is that space and time are continuous, and that the laws of nature are described by differential equations. There are, of course, exceptions: chemistry, statistical mechanics, and quantum physics are based on at least a certain degree of discreteness. But these discrete objects (molecules, atoms, elementary particles, Feynman graphs) live in the continuum of space and time. String theory tries to explain these discrete objects as singularities of a higher dimensional continuum.
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NEWTON’S METHOD The Golden Section Search method requires explicitly indicating lower and upper boundaries for the search region in which the optimal solution lies. Such methods where the boundaries need to be specified are known as bracketing
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