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Webster R. — Convexity
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Название: ConvexityАвтор: Webster R. Аннотация: This text provides a comprehensive introduction to convex sets and functions. Requiring only a basic knowledge of analysis and linear algebra, the book clearly discusses topics as diverse as number theory, classical extremum problems, combinatorial geometry, linear programming, game theory, polytopes, bodies of constant width, the gamma function, minimax approximation, and the theory of linear, classical, and matrix inequalities. The book clearly shows how convexity links many different topics in mathematics, from linear algebra to analysis. Suitable for upper-level undergraduate and graduate students, this book offers full solutions to over 200 exercises as well as detailed suggestions for further reading.
Язык: Рубрика: Математика /Геометрия и топология /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1994Количество страниц: 464Добавлена в каталог: 18.04.2005Операции: Положить на полку |
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Minimal width 368 Minimax approximation 324 Minimax theorem 181 185 Minimization of quadratic forms 353 354 Minkowski, H. 350 353 354 Minkowski’s determinant inequality 250 Minkowski’s inequality 202 203 223 Minkowski’s inequality for mixed volumes 300 Minkowski’s theorem 351 Mixed volumes 281 286 Mixed volumes, continuity of 289 Moment curve 120 Motzkin, T. S. 362 Motzkin’s theorem 362 364 n-dimensional space 1 n-volume 274 Nearest points 46 47 Neighbourhood 91 Neighbourly polytope 120 125 Non-basic variable 172 Non-degeneracy condition 171 172 179 Non-degenerate cell 298 Non-negative orthant 75 Non-negative quadrant 74 Non-singular affine transformation 24 Norm mapping 44 221 Norm of a vector 26 Normal vector 27 Obtuse angle 27 Ohmann, D. 297 One-sided derivative 226 Open ball 32 Open disc 32 Open halfspace 20 Open set 33 Open unit ball 32 Optimal strategy 184 185 Optimal vector 157 160 165 Origin 2 Orthogonal complement 27 Orthogonal vectors 27 Orthonormal sequence 27 Orthotope 119 Outer parallel set 91 Outer-volume 262 Outward normal 234 Parallelism 6 16 Parallelotope 119 Parallelotope, volume 274 Partial derivative 225 Pay-off matrix 181 Peano’s postulate 332 Perimeter function 296 Permutation matrix 246 Perron — Frobenius theorem 362 Perron, O. 362 Pivot 169 Pivoting 169 Play of a game 181 Poincare, H. 127 Point 1 2 Polar dual 99 Polar face mapping 102 Polyhedral cone 145 Polyhedral set 110 Polytope 105 Positive diagonal 250 Positively homogeneous function 221 Primal problem 160 Primitive set 83 prism 118 119 Prism construction 119 Projection of a point 363 Projection of a set 307 Projection operator 66 363 Proper face 80 Pure strategy 182 Pyramid 116 117 Quadratic function 245 Quadratic programming problem 244 Quasi-convex function 223 r-bipyramid 117 r-crosspolytope 105 118 r-cube 107 119 r-flat 14 r-orthotope 118 r-parallelotope 119 r-polytope 105 r-prism 119 r-pyramid 116 r-simplex 105 Rademacher, H. 318 Radius of a ball 32 Radon’s theorem 56 60 317 Ray 74 Real n-tuple 1 Recession cone 74 76 Regular cross polytope 105 Regular octahedron 106 Regular polytope 133 Relative boundary 37 Relative boundary, point 37 Relative interior 37 Relative interior, point 37 retract 366 Reuleaux triangle 370 Riemann integrable 275 Riemann integral 274 Root mean square 203 204 Row player 181 s-fold r-bipyramid 118 s-fold r-prism 119 s-fold r-pyramid 117 Saddle point 188 240 Saddle-point problem 239 240 scalar 1 Scalar multiple 2 Scalar multiplication 2 Schoenberg, I. J. 318 Schwarz rotation symmetral 304 305 Schwarz, H. A. 304 306 Security level 184 Separation 65 68 Separation, proper 68 Separation, strict 68 simplex 105 Simplex algorithm 168 169 171 Simplex, volume 278 Simplicial polytope 121 Slack variable 166 Soluble problem 157 160 Solution set 16 Solution to game 186 Solution to linear inequalities 153 Sperner, E. 357 Sperner’s lemma 360 Standard join 364 Standard maximum problem 157 Standard minimum problem 160 Starcentre 321 336 Starshaped set 321 Steiner symmetral 307 309 Steiner symmetrization 306 310 Steiner symmetrization, continuity of 312 Stelner, J. 306 Stirling’s formula 213 214 Straszewicz’s theorem 89 Strategy 182 subspace 5 Subtraction of vectors 2 Sun 364 Support function 231—238 Support hyperplane 71 Support hyperplane to a closed ball 72 Support hyperplane, non-trivial 71 Support of a function 197 220 Surface area 294 295 Symmetric set 3 Symmetric set, 0-symmetric set 2 Tableau 171 173 175 Tableau, final 133 175 Tableau, initial 172 175 Tailor’s problem 158 160 166 169 175 Theory of games 181 Three chords lemma 194 Topological equivalence 366 translate 3 Translation 22 Transposition law 332 Transveral 317 Triangle inequality 36 Tsu Ch’ung-chi 355 Uniform boundedness 96 Unique farthest-point property 365 Unit vector 26 Upper Bound Theorem 120 Upper integral 275 Upper sum 275 Valentine, F. A. 318 Value of game 184 185 186 Value of problem 157 160 Vandermonde’s determinant 121 Vector 1 2 Vector sum 2 Vertex 107 Vertex set 107 Visible point 321 Volume 257 260 263 Volume of ball 278 279 Volume of cell 257 Volume of conical set 276 277 Volume of cylindrical set 276 277 Volume of elementary set 260 Volume of ellipsoid 279 Volume of parallelotope 274 Volume of polytope 279 Volume of simplex 278 Volume, inner 262 Volume, mixed 281 286 Volume, outer 262 von Neumann’s minimax theorem 181 185 Wahun, G. E. 320 Wallis’ formula 216 Weierstrass’ formula 216 Weighted mean 201 204 width 367 368 Width in a direction 368 Width, maximal 368 Width, minimal 368 Zero vector 2 Zonotope 107
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