Presentation of the Mumford-Shah Functional -- Functions in the Sobolev Spaces W1,p -- Regularity Properties for Quasiminimizers -- Limits of Almost-Minimizers -- Pieces of C1 Curves for Almost-Minimizers -- Global Mumford-Shah Minimizers in the Plane -- Applications to Almost-Minimizers (n = 2) -- Quasi- and Almost-Minimizers in Higher Dimensions -- Boundary Regularity.Award-winning monograph …
Two Classical Optimization Problems -- Gauss’ Question -- What Does Solution Mean? -- Network Design Problems -- A New Challenge: The Phylogeny -- An Analysis of Steiner’s Problem in Phylogenetic Spaces -- Tree Building Algorithms.The problem of "Shortest Connectivity" has a long and convoluted history: given a finite set of points in a metric space, search for a network that connects these…
Classical Techniques -- Integer Programming -- Genetic Algorithms -- Genetic Programming -- Tabu Search -- Simulated Annealing -- Variable Neighborhood Search -- Constraint Programming -- Multi-Objective Optimization -- Complexity Theory and the No Free Lunch Theorem -- Machine Learning -- Artificial Immune Systems -- Swarm Intelligence -- Fuzzy Reasoning -- Rough Set Based Decision Support -- …
Quadratic Programming Problems -- Existence Theorems for Quadratic Programs -- Necessary and Sufficient Optimality Conditions for Quadratic Programs -- Properties of the Solution Sets of Quadratic Programs -- Affine Variational Inequalities -- Solution Existence for Affine Variational Inequalities -- Upper-Lipschitz Continuity of the Solution Map in Affine Variational Inequalities -- Linear Fra…
Line Search Descent Methods for Unconstrained Minimization -- Standard Methods for Constrained Optimization -- New Gradient-Based Trajectory and Approximation Methods -- Example Problems -- Some Theorems.This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form without neglecting rigour. The work should enable the prof…
Duality and Optimality Conditions -- On Minimization of Max-Min Functions -- A Comparison of Two Approaches to Second-Order Subdifferentiability Concepts with Application to Optimality Conditions -- Duality and Exact Penalization via a Generalized Augmented Lagrangian Function -- Duality for Semi-Definite and Semi-Infinite Programming with Equality Constraints -- The Use of Nonsmooth Analysis a…
Control of Systems Described by Elliptic-Type Partial-Differential Equations under Conjugation Conditions -- Control of a Conditionally Correct System Described by the Neumann Problem for an Elliptic-Type Equation under Conjugation Conditions -- Control of a System Described by a One-Dimensional Quartic Equation under Conjugation Conditions -- Control of a System Described by a Two-Dimensional …
Optimal Control Models in Finance -- The STV Approach to Financial Optimal Control Models -- A Financial Oscillator Model -- An Optimal Corporate Financing Model -- Further Computational Experiments and Results -- Conclusion.The determination of optimal financing and investment strategies (optimal capital structure or optimal mix of funds, optimal portfolio choice, etc.) for corporations and th…
Batch Presorting Problems. I Models and Solution Approaches -- Batch Presorting Problems. II Applications in Inventory Logistics -- Vehicle Routing Problems in Hospital Transportation. I Models and Solution Approaches -- Vehicle Routing Problems in Hospital Transportation. II Applications and Case Studies -- Summary.This books covers the analysis and development of online algorithms involving e…
Portfolio Optimization -- One-Variable Optimization -- Optimal Portfolios with N Assets -- Unconstrained Optimization in N Variables -- The Steepest Descent Method -- The Newton Method -- Quasi-Newton Methods -- Conjugate Gradient Methods -- Optimal Portfolios with Restrictions -- Larger-Scale Portfolios -- Data-Fitting & The Gauss-Newton Method -- Equality Constrained Optimization -- Linear Eq…