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The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science.
The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science.
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First Sentence:
This chapter presents a brief summary of the standard terminology and basic results related to characterizing the maximal and minimal values of a real valued function f defined on a set D in Euclidean space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
local extremal point, possible corner points, maximal row rank, implicit function theory, transversal condition, stationary family, stationary functions, extremal function, saddle function, reverse triangle inequality, local extremals, weak local minimum, stationary trajectory, elementary convexity, unique optimal control, strong local minimum, stationary trajectories, exact field, sufficient differentiability, brachistochrone problem, convexity methods, minimizing function, end point conditions, normed linear space, local minimum point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Jakob Bernoulli, Johann Bernoulli, Review of Optimization, Standard Optimization Problems, The Weierstrass-Erdmann Corner Conditions, Construction of Central Fields, The Zenodoros Problem, Variable End Point Problems New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter presents a brief summary of the standard terminology and basic results related to characterizing the maximal and minimal values of a real valued function f defined on a set D in Euclidean space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
local extremal point, possible corner points, maximal row rank, implicit function theory, transversal condition, stationary family, stationary functions, extremal function, saddle function, reverse triangle inequality, local extremals, weak local minimum, stationary trajectory, elementary convexity, unique optimal control, strong local minimum, stationary trajectories, exact field, sufficient differentiability, brachistochrone problem, convexity methods, minimizing function, end point conditions, normed linear space, local minimum point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Jakob Bernoulli, Johann Bernoulli, Review of Optimization, Standard Optimization Problems, The Weierstrass-Erdmann Corner Conditions, Construction of Central Fields, The Zenodoros Problem, Variable End Point Problems New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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1
book
cites this book:
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter (1), Back Matter (2), and Back Matter (3)
- Calculus of Variations by I. M. Gelfand in Back Matter (1), and Back Matter (2)
- Calculus of Variations (Carus Monograph) by Gilbert Ames Bliss in Back Matter (1), and Back Matter (2)
- Functions of Several Variables (Undergraduate Texts in Mathematics) by Wendell Fleming in Front Matter, and Back Matter
- Calculus of Variations by Rund in Back Matter
See all 100 books this book cites
- Frontiers in Global Optimization (Nonconvex Optimization and Its Applications) by Christodoulos A. Floudas on page 497
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