optimization

optimization
Optimization?

A farmer wants to fence an area of 1.5 million square feet in a rectangular field and divide it in half with a fence parallel to one of those sides of the rectangle. How can he do this so as to minimize the cost of the fence?

I have no idea how to do this. I’m terrible at optimization…

If you can help, I would gladly appreciate it!

Not sure if I understood your problem.

To divide the rectangular in half with a fence parallel to one of its sides, the fence must join the the medium points of the other 2 sides. So, it’s immediate that, in order to minimize the cost (so the total length) of the fence, it should be parallel to the smallest t side.

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Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theor
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Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theor
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Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theor
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Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically. This introduction to optimization attempts to strike a balance between presentation of mathematical theor
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Finite-dimensional optimization problems occur throughout the mathematical sciences. The majority of these problems cannot be solved analytically...
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This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant.
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This book covers algorithms and discretization procedures for the solution of nonlinear progamming, semi-infinite optimization and optimal control problems. Among the important features included are the theory of algorithms represented as point-to-set maps, the treatment of min-max problems with and without constraints, the theory of consistent approximation which provides a framework for the solution of semi-infinite optimization, optimal control, and shape optimization problems with very general constraints, using simple algorithms that call standard nonlinear programming algorithms as subroutines, the completeness with which algorithms are analysed, and chapter 5 containing mathematical results needed in optimization from a large assortment of sources. Readers will find of particular interest the exhaustive modern treatment of optimality conditions and algorithms for min-max problems, as well as the newly developed theory of consistent approximations and the treatment of semi-infinite optimization and optimal control problems in this framework. This book presents the first treatment of optimization algorithms for optimal control problems with state-trajectory and control constraints, and fully accounts for all the approximations that one must make in their solution.It is also the first to make use of the concepts of epi-convergence and optimality functions in the construction of consistent approximations to infinite dimensional problems.
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Well written and well organized. The book''s examples are highly varied, interesting and well thought out. --Steinar Hauan, Carnegie Mellon University An extremely interesting introduction to the field of mathematical optimization. I know of no other book in the field that offers so many illustrations of the applicability of deep theoretical issues in optimization. It will command a broad audience, from beginners to experts. --Kees Roos, Delft University of Technology
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