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Equilibrium Problems and Variational Models

Aus der Reihe Nonconvex Optimization and Its Applications

97,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

17.09.2011

Herausgeber

P. Daniele + weitere

Verlag

Springer Us

Seitenzahl

446

Maße (L/B/H)

23,5/15,5/2,5 cm

Gewicht

692 g

Auflage

Softcover reprint of the original 1st ed. 2003

Sprache

Englisch

ISBN

978-1-4613-7955-3

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

17.09.2011

Herausgeber

Verlag

Springer Us

Seitenzahl

446

Maße (L/B/H)

23,5/15,5/2,5 cm

Gewicht

692 g

Auflage

Softcover reprint of the original 1st ed. 2003

Sprache

Englisch

ISBN

978-1-4613-7955-3

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

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  • Produktbild: Equilibrium Problems and Variational Models
  • Produktbild: Equilibrium Problems and Variational Models
  • On Vector Quasi—Equilibrium Problems.- 1. Introduction.- 2. Preliminaries.- 3. Existence Results.- 4. Some Applications.- References.- The Log-Quadratic Proximal Methodology in Convex Optimization Algorithms and Variational Inequalities.- 1. Introduction.- 2. Lagrangians and Proximal Methods.- 2.1. The quadratic augmented Lagrangian.- 2.2. Proximal Minimization Algorithms.- 2.3. Entropic Proximal Methods and Modified Lagrangians.- 2.4. Difficulties with Entropic Proximal Methods.- 2.5. Toward Solutions to Difficulties.- 3. The Logarithmic-Quadratic Proximal Framework.- 3.1. The LQ-Function and its Conjugate: Basic Properties.- 3.2. The Logarithmic-Quadratic Proximal Minimization.- 4. The LQP in Action.- 4.1. Primal LQP for Variational Inequalities over Polyhedra.- 4.2. Lagrangian Methods for convex optimization and variational inequalities.- 4.3. Dual and Primal-Dual Decomposition schemes.- 4.4. Primal Decomposition: Block Gauss-Seidel Schemes for Linearly constrained Problems.- 4.5. Convex Feasibility Problems.- 4.6. Bundle Methods in Nonsmooth Optimization.- References.- The Continuum Model of Transportation Problem.- 1. Introduction.- 2. Calculus of the solution.- References.- The Economic Model for Demand—Supply Problems.- 1. Introduction.- 2. The first phase: formalization of the equilibrium.- 3. The second phase: formalization of the equilibrium.- 4. The dependence of the second phase on the first one.- 5. General model.- 6. Example.- References.- Constrained Problems of Calculus of Variations Via Penalization Technique.- 1. Introduction.- 2. Statement of the problem.- 3. An equivalent statement of the problem.- 4. Local minima.- 5. Penalty functions.- 6. Exact penalty functions.- 6.1. Properties of the function ?.- 6.2. Properties of the function G.- 6.3. The rate of descent of the function ?.- 6.4. An Exact Penalty function.- 7. Necessary conditions for an Extremum.- 7.1. Necessary conditions generated by classical variations.- 7.2. Discussion and Remarks.- References.- Variational Problems with Constraints Involving Higher—Order Derivatives.- 1. Introduction.- 2. Statement of the problem.- 3. An equivalent statement of the problem.- 4. Local minima.- 5. Properties of the function ?.- 5.1. A classical variation of z.- 5.2. The case z ? Z.- 5.3. The case z ? Z.- 6. Exact penalty functions.- 6.1. Properties of the function G.- 6.2. An Exact Penalty function.- 7. Necessary conditions for an Extremum.- References.- On the strong solvability of a unilateral boundary value problem for Nonlinear Parabolic Operators in the Plane.- 1. Introduction.- 2. Hypotheses and results.- 3. Preliminary results.- 4. Proof of the theorems.- References.- Solving a Special Class of Discrete Optimal Control Problems Via a Parallel Interior—Point Method.- 1. Introduction.- 2. Framework of the Method.- 3. Global convergence.- 4. A special class of discrete optimal control problems.- 5. Numerical experiments.- 6. Conclusions.- References.- Solving Large Scale Fixed Charge Network Flow Problems.- 1. Introduction.- 2. Problem Definition and Formulation.- 3. Solution Procedure.- 3.1. The DSSP.- 3.2. Local Search.- 4. Computational Results.- 5. Concluding Remarks.- References.- Variable Projection Methods for Large—Scale Quadratic Optimization in data Analysis Applications.- 1. Introduction.- 2. Large QP Problems in Training Support Vector Machines.- 3. Numerical Solution of Image Restoration Problem.- 4. A Bivariate Interpolation Problem.- 5. Conclusions.- References.- Strong solvability of boundary value problems in elasticity with Unilateral Constraints.- 1. Introduction.- 2. Basic assumptions and main results.- 3. Preliminary results.- 4. Proof of the theorems.- References.- Time Dependent Variational Inequalities — Some Recent Trends.- 1. Introduction.- 2. Time - an additional parameter in variational inequalities.- 2.1. Time-dependent variational inequalities and quasi-variational inequalities.- 2.2. Some classic results on the differentiability of the projection on closed convex subsets in Hilbert space.- 2.3. Time-dependent variational inequalities with memory terms.- 3. Ordinary Differential Inclusions with Convex Constraints: Sweeping Processes.- 3.1. Moving convex sets and systems with hysteresis.- 3.2. Sweeping processes and generalizations.- 4. Projected dynamical systems.- 4.1. Differentiability of the projection onto closed convex subsets revisited.- 4.2. Projected dynamical systems and stationarity.- 4.3. Well-posedness for projected dynamical systems.- 5. Some Asymptotic Results.- 5.1. Some classical results.- 5.2. An asymptotic result for full discretization.- 5.3. Some convergence results for continuous-time subgradient procedures for convex optimization.- References.- On the Contractibility of the Efficient and Weakly Efficient Sets in R2.- 1. Introduction.- 2. Preliminaries.- 3. Topological structure of the efficient sets of compact convex sets.- 4. Example.- References.- Existence Theorems for a Class of Variational Inequalities and Applications to a Continuous Model of Transportation.- 1. Introduction.- 2. Continuous transportation model.- 3. Existence Theorem.- References.- On Auxiliary Principle for Equilibrium Problems.- 1. Introduction.- 2. The auxiliary equilibrium problem.- 3. The auxiliary problem principle.- 4. Applications to variational inequalities and optimization problems.- 5. Concluding remarks.- References.- Multicriteria Spatial Price Networks: Statics and Dynamics.- 1. Introduction.- 2. The Multicriteria Spatial Price Model.- 3. Qualitative Properties.- 4. The Dynamics.- 5. The Discrete-Time Algorithm.- 6. Numerical Examples.- 7. Summary and Conclusions.- References.- Non regular data in unilateral variational problems.- 1. Introduction.- 2. The approach by truncation and approximation.- 3. Renormalized formulation.- 4. Multivalued operators and more general measures.- 5. Uniqueness and convergence.- References.- Equilibrium Concepts in Transportation Networks: Generalized Wardrop Conditions and Variational Formulations.- 1. Introduction.- 2. Equilibrium model in a traffic network.- References.- Variational Geometry and Equilibrium.- 1. Introduction.- 2. Variational Inequalities and Normals to Convex Sets.- 3. Quasi-Variational Inequalities and Normals to General Sets.- 4. Calculus and Solution Perturbations.- 5. Application to an Equilibrium Model with Aggregation.- References.- On the Calculation of Equilibrium in Time Dependent Traffic Networks.- 1. Introduction.- 2. Calculation of Equilibria.- 3. The algorithm.- 4. Applications and Examples.- 5. Conclusions.- References.- Mechanical Equilibrium and Equilibrium Systems.- 1. Introduction.- 2. Physical motivation.- 3. Statement of the mechanical force equilibrium problem.- 4. The principle of virtual work.- 5. Characterization of the constraints.- 6. Quasi-variational inequalities (QVI).- 7. Principle of virtual work in force fields under scleronomic and holonomic constraints.- 8. Dual form of the principle of virtual work in force field under scleronomic and holonomic constraints.- 9. Procedure for solving mechanical equilibrium problems.- 10. Existence of solutions.- References.- False Numerical Convergence in Some Generalized Newton Methods.- 1. Introduction.- 2. Some generalized Newton methods.- 3. False numerical convergence.- 4. An example.- 5. Avoiding false numerical convergence.- References.- Distance to the Solution Set of an Inequality with an Increasing Function.- 1. Introduction.- 2. Preliminaries.- 3. Distance to the solution set of the inequality with an arbitrary increasing function.- 4. Distance to the solution set of the inequality with an ICAR function.- 5. Inequalities with an increasing function defined on the entire space.- 6. Inequalities with a topical function.- References.- Transportation Networks with Capacity Constraints.- 1. Introduction.- 2. Wardrop’s generalized equilibrium condition.- 3. A triangular network.- 4. More about generalized equilibrium principle.- 5. Capacity constraints and paradox.- References.