| Preface | p. xiii |
| On Vector Quasi-Equilibrium Problems | p. 1 |
| Introduction | p. 1 |
| Preliminaries | p. 3 |
| Existence Results | p. 6 |
| Some Applications | p. 10 |
| References | p. 15 |
| The Log-Quadratic Proximal Methodology in Convex Optimization Algorithms and Variational Inequalities | p. 19 |
| Introduction | p. 20 |
| Lagrangians and Proximal Methods | p. 21 |
| The Logarithmic-Quadratic Proximal Framework | p. 29 |
| The LQP in Action | p. 33 |
| References | p. 45 |
| The Continuum Model of Transportation Problem | p. 53 |
| Introduction | p. 53 |
| Calculus of the solution | p. 56 |
| References | p. 59 |
| The Economic Model for Demand-Supply Problems | p. 61 |
| Introduction | p. 61 |
| The first phase: formalization of the equilibrium | p. 62 |
| The second phase: formalization of the equilibrium | p. 67 |
| The dependence of the second phase on the first one | p. 70 |
| General model | p. 71 |
| Example | p. 72 |
| References | p. 77 |
| Constrained Problems of Calculus of Variations Via Penalization Technique | p. 79 |
| Introduction | p. 79 |
| Statement of the problem | p. 80 |
| An equivalent statement of the problem | p. 81 |
| Local minima | p. 83 |
| Penalty functions | p. 86 |
| Exact penalty functions | p. 88 |
| Necessary conditions for an Extremum | p. 100 |
| References | p. 106 |
| Variational Problems with Constraints Involving Higher-Order Derivatives | p. 109 |
| Introduction | p. 109 |
| Statement of the problem | p. 110 |
| An equivalent statement of the problem | p. 111 |
| Local minima | p. 114 |
| Properties of the function [open phi] | p. 115 |
| Exact penalty functions | p. 123 |
| Necessary conditions for an Extremum | p. 127 |
| References | p. 133 |
| On the strong solvability of a unilateral boundary value problem for Nonlinear Parabolic Operators in the Plane | p. 135 |
| Introduction | p. 135 |
| Hypotheses and results | p. 136 |
| Preliminary results | p. 137 |
| Proof of the theorems | p. 138 |
| References | p. 140 |
| Solving a Special Class of Discrete Optimal Control Problems Via a Parallel Interior-Point Method | p. 141 |
| Introduction | p. 142 |
| Framework of the Method | p. 143 |
| Global convergence | p. 149 |
| A special class of discrete optimal control problems | p. 152 |
| Numercial experiments | p. 157 |
| Conclusions | p. 160 |
| References | p. 160 |
| Solving Large Scale Fixed Charge Network Flow Problems | p. 163 |
| Introduction | p. 164 |
| Problem Definition and Formulation | p. 166 |
| Solution Procedure | p. 167 |
| Computational Results | p. 171 |
| Concluding Remarks | p. 181 |
| References | p. 181 |
| Variable Projection Methods for Large-Scale Quadratic Optimization in data Analysis Applications | p. 185 |
| Introduction | p. 185 |
| Large QP Problems in Training Support Vector Machines | p. 188 |
| Numerical Solution of Image Restoration Problem | p. 193 |
| A Bivariate Interpolation Problem | p. 200 |
| Conclusions | p. 206 |
| References | p. 207 |
| Strong solvability of boundary value problems in elasticity with Unilateral Constraints | p. 213 |
| Introduction | p. 213 |
| Basic assumptions and main results | p. 215 |
| Preliminary results | p. 217 |
| Proof of the theorems | p. 218 |
| References | p. 223 |
| Time Dependent Variational Inequalities--Some Recent Trends | p. 225 |
| Introduction | p. 226 |
| Time - an additional parameter in variational inequalities | p. 229 |
| Ordinary Differential Inclusions with Convex Constraints: Sweeping Processes | p. 240 |
| Projected dynamical systems | p. 247 |
| Some Asymptotic Results | p. 252 |
| References | p. 259 |
| On the Contractibility of the Efficient and Weakly Efficient Sets in R[superscript 2] | p. 265 |
| Introduction | p. 265 |
| Preliminaries | p. 266 |
| Topological structure of the efficient sets of compact convex sets | p. 267 |
| Example | p. 276 |
| References | p. 278 |
| Existence Theorems for a Class of Variational Inequalities and Applications to a Continuous Model of Transportation | p. 281 |
| Introduction | p. 281 |
| Continuous transportation model | p. 282 |
| Existence Theorem | p. 284 |
| References | p. 287 |
| On Auxiliary Principle for Equilibrium Problems | p. 289 |
| Introduction | p. 289 |
| The auxiliary equilibrium problem | p. 291 |
| The auxiliary problem principle | p. 293 |
| Applications to variational inequalities and optimization problems | p. 295 |
| Concluding remarks | p. 297 |
| References | p. 297 |
| Multicriteria Spatial Price Networks: Statics and Dynamics | p. 299 |
| Introduction | p. 299 |
| The Multicriteria Spatial Price Model | p. 301 |
| Qualitative Properties | p. 306 |
| The Dynamics | p. 309 |
| The Discrete-Time Algorithm | p. 311 |
| Numerical Examples | p. 314 |
| Summary and Conclusions | p. 318 |
| References | p. 319 |
| Non regular data in unilateral variational problems | p. 323 |
| Introduction | p. 323 |
| The approach by truncation and approximation | p. 324 |
| Renormalized formulation | p. 328 |
| Multivalued operators and more general measures | p. 328 |
| Uniqueness and convergence | p. 330 |
| References | p. 331 |
| Equilibrium Concepts in Transportation Networks: Generalized Wardrop Conditions and Variational Formulations | p. 333 |
| Introduction | p. 333 |
| Equilibrium model in a traffic network | p. 334 |
| References | p. 344 |
| Variational Geometry and Equilibrium | p. 347 |
| Introduction | p. 347 |
| Variational Inequalities and Normals to Convex Sets | p. 349 |
| Quasi-Variational Inequalities and Normals to General Sets | p. 352 |
| Calculus and Solution Perturbations | p. 357 |
| Application to an Equilibrium Model with Aggregation | p. 361 |
| References | p. 367 |
| On the Calculation of Equilibrium in Time Dependent Traffic Networks | p. 369 |
| Introduction | p. 369 |
| Calculation of Equilibria | p. 370 |
| The algorithm | p. 371 |
| Applications and Examples | p. 372 |
| Conclusions | p. 376 |
| References | p. 376 |
| Mechanical Equilibrium and Equilibrium Systems | p. 379 |
| Introduction | p. 379 |
| Physical motivation | p. 380 |
| Statement of the mechanical force equilibrium problem | p. 381 |
| The principle of virtual work | p. 382 |
| Characterization of the constraints | p. 383 |
| Quasi-variational inequalities (QVI) | p. 384 |
| Principle of virtual work in force fields under scleronomic and holonomic constraints | p. 385 |
| Dual form of the principle of virtual work in force field under scleronomic and holonomic constraints | p. 388 |
| Procedure for solving mechanical equilibrium problems | p. 391 |
| Existence of solutions | p. 395 |
| References | p. 397 |
| False Numerical Convergence in Some Generalized Newton Methods | p. 401 |
| Introduction | p. 401 |
| Some generalized Newton methods | p. 402 |
| False numerical convergence | p. 405 |
| An example | p. 408 |
| Avoiding false numerical convergence | p. 411 |
| References | p. 415 |
| Distance to the Solution Set of an Inequality with an Increasing Function | p. 417 |
| Introduction | p. 417 |
| Preliminaries | p. 418 |
| Distance to the solution set of the inequality with an arbitrary increasing function | p. 420 |
| Distance to the solution set of the inequality with an ICAR function | p. 423 |
| Inequalities with an increasing function defined on the entire space | p. 427 |
| Inequalities with a topical function | p. 429 |
| References | p. 430 |
| Transportation Networks with Capacity Constraints | p. 433 |
| Introduction | p. 433 |
| Wardrop's generalized equilibrium condition | p. 434 |
| A triangular network | p. 436 |
| More about generalized equilibrium principle | p. 438 |
| Capacity constraints and paradox | p. 442 |
| References | p. 443 |
| Table of Contents provided by Ingram. All Rights Reserved. |