| Preface |
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xv | |
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Linear Semi-infinite Optimization: Recent Advances |
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3 | (20) |
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3 | (2) |
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Linear semi-infinite systems |
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5 | (3) |
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8 | (3) |
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11 | (2) |
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13 | (10) |
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17 | (6) |
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Some Theoretical Aspects of Newton's Method for Constrained Best Interpolation |
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23 | (228) |
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23 | (3) |
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Constrained Interpolation in Hilbert Space |
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26 | (5) |
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Nonsmooth Functions and Equations |
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31 | (2) |
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Newton's Method and Convergence Analysis |
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33 | (12) |
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33 | (3) |
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36 | (3) |
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39 | (3) |
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Application to Inequality Constraints |
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42 | (2) |
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44 | (1) |
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45 | (172) |
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46 | (171) |
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Optimization: the Cutting Angle method |
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217 | (7) |
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217 | (1) |
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The Cutting Angle algorithm |
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218 | (1) |
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Enumeration of local minima |
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219 | (3) |
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222 | (1) |
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223 | (1) |
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Random variate generation: acceptance/ rejection |
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224 | (11) |
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224 | (2) |
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226 | (1) |
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Univariate Lipschitz densities |
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227 | (3) |
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Lipschitz densities in Rn |
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230 | (1) |
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Description of the algorithm |
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231 | (2) |
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233 | (2) |
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Scattered data interpolation: Lipschitz approximation |
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235 | (9) |
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235 | (2) |
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Best uniform approximation |
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237 | (1) |
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Description of the algorithm |
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238 | (2) |
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240 | (4) |
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244 | (7) |
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244 | (7) |
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Part II Theory and Numerical Methods |
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A Numerical Method for Concave Programming Problems |
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251 | (24) |
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251 | (1) |
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Global Optimality Condition |
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252 | (2) |
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Approximation Techniques of the Level Set |
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254 | (8) |
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Algorithms and their Convergence |
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262 | (8) |
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270 | (2) |
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272 | (3) |
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272 | (3) |
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Convexification and Monotone Optimization |
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275 | (18) |
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275 | (1) |
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Monotonicity and convexity |
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276 | (5) |
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Monotone optimization and concave minimization |
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281 | (2) |
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Equivalence to concave minimization |
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281 | (1) |
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Outer approximation algorithm for concave minimization problems |
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281 | (2) |
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Polyblock outer approximation method |
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283 | (3) |
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286 | (2) |
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288 | (1) |
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289 | (4) |
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289 | (4) |
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Generalized Lagrange Multipliers for Nonconvex Directionally Differentiable Programs |
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293 | (28) |
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Introduction and Preliminaries |
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293 | (3) |
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Generalized Lagrange Multipliers |
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296 | (8) |
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Necessary conditions for optimality |
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296 | (5) |
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Sufficient condition for optimality |
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301 | (3) |
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Special Cases and Applications |
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304 | (10) |
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Problems with convexlike directional derivatives |
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304 | (1) |
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Composite nonsmooth programming with Gateaux differentiability |
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305 | (4) |
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Quasidifferentiable problems |
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309 | (5) |
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Directionally Differentiable Problems with DSL-approximates |
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314 | (7) |
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317 | (4) |
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Slice Convergence of Sums of Convex functions in Banach Spaces and Saddle Point Convergence |
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321 | (22) |
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321 | (2) |
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323 | (4) |
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A Sum Theorem for Slice Convergence |
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327 | (9) |
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Saddle-point Convergence in Fenchel Duality |
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336 | (7) |
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341 | (2) |
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Topical Functions and their Properties in a Class of Ordered Banach Spaces |
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343 | (22) |
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343 | (1) |
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344 | (3) |
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Plus-Minkowski gauge and plus-weak Pareto point for a downward set |
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347 | (2) |
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Xφ-subdifferential of a topical function |
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349 | (4) |
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Fenchel-Moreau conjugates with respect to φ |
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353 | (4) |
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Conjugate of type Lau with respect to φ |
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357 | (8) |
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360 | (5) |
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Dynamical Systems Described by Relational Elasticities with Applications |
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365 | (22) |
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365 | (2) |
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Relationship between two variables: relational elasticity |
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367 | (2) |
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Some examples for calculating relational elasticities |
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369 | (1) |
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370 | (4) |
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Classification Algorithm based on a dynamical systems approach |
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374 | (3) |
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Algorithm for global optimization |
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377 | (3) |
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Results of numerical experiments |
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380 | (1) |
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Conclusions and future work |
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381 | (6) |
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383 | (4) |
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Impulsive Control of a Sequence of Rumour Processes |
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387 | (22) |
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387 | (2) |
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Single-Rumour Process and Preliminaries |
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389 | (2) |
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391 | (4) |
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395 | (4) |
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399 | (3) |
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402 | (3) |
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405 | (4) |
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406 | (3) |
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Minimization of the Sum of Minima of Convex Functions and Its Application to Clustering |
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409 | (26) |
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409 | (1) |
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A class of sum-min functions |
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410 | (1) |
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Functions represented as the sum of minima of convex functions |
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410 | (1) |
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Some properties of functions belonging to F |
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411 | (1) |
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411 | (4) |
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Cluster functions and generalized cluster functions |
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412 | (1) |
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Bradley-Mangasarian approximation of a finite set |
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412 | (1) |
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Skeleton of a finite set of points |
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413 | (1) |
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414 | (1) |
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Minimization of sum-min functions belonging to class F |
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415 | (2) |
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Minimization of generalized cluster function |
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417 | (2) |
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Construction of generalized cluster functions |
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417 | (1) |
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418 | (1) |
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Numerical experiments with generalized cluster function |
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419 | (5) |
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419 | (1) |
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Numerical experiments: description |
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419 | (1) |
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Results of numerical experiments |
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420 | (4) |
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424 | (6) |
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424 | (3) |
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Numerical experiments: description |
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427 | (2) |
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Numerical experiments: results |
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429 | (1) |
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430 | (1) |
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430 | (5) |
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430 | (1) |
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431 | (2) |
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433 | (2) |
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Analysis of a Practical Control Policy for Water Storage in Two Connected Dams |
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435 | (15) |
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435 | (1) |
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436 | (2) |
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Intuitive calculation of the invariant probability |
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438 | (2) |
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Existence of the inverse matrices |
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440 | (1) |
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441 | (4) |
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The expected long-term overflow |
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445 | (1) |
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Extension of the fundamental ideas |
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445 | (5) |
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450 | |
Lisainfo e-raamatute kohta