E-raamat: Progress in Optimization: Contributions from Australasia

Preface xi Participants xv Editors xix Part I GLOBAL OPTIMIZATION Global Optimization Methods for Location and Distance Geometry Problems 3(18) Hoang Tuy Introduction 4(1) Global Optimization 5(1) A Generic BB Method 6(2) The Generalized Webers Problem 8(1) Various Objectives in Facility Location 9(3) Constrained Location 12(2) Challenging Problems 14(3) Conclusions 17(4) References 17(4) Branch and Cut Methods for Mixed Integer Linear Programming Problems 21(24) Louis Caccetta Introduction 22(1) Solution Methods 23(5) The Traveling Salesman Problem 28(2) Vehicle Routing Problem 30(5) A Mine Scheduling Problem 35(4) Conclusions 39(6) References 39(6) Separability of Star-Shaped Sets with Respect to Infinity 45(20) A. M. Rubinov A. P. Shveidel Introduction 46(1) Preliminaries 47(1) Strongly Star-Shaped Sets 48(4) Separation 52(8) Sum of Strongly Star-Shaped Sets w.r.t. Infinity 60(2) Separation of Strongly Star-Shaped Sets w.r.t. Infinity 62(3) References 63(2) Nonlinear Unconstrained Optimization Methods: A Review 65(14) A. M. Rubinov X. Q. Yang B. M. Glover Introduction 66(1) Nonlinear Penalty Functions 67(2) Penalty Functions for Problems with One Constraint 69(1) Nonlinear Lagrangian Functions 70(2) Lagrange Functions for Problems with One Constraint 72(1) Penalty and Lagrange 73(1) Parameter Nonlinear Unconstrained Optimization Methods 74(5) References 77(2) New Dual Formulations in Constrained Integer Programming 79(14) Xiaoling Sun Duan Li Introduction 80(1) Duality Gap in the Classical Lagrangian Method 80(4) p-norm Surrogate Constraint Method 84(1) p-th Power Lagrangian Method 85(1) Minimax-type Lagrangian Function 86(1) Logarithmic-exponential Dual Formulation 87(3) Conclusions 90(3) References 90(3) Simulated Annealing and Penalty Methods for Binary Multicommodity Flow Problems 93(16) X. Q. Yang A. I. Mees K. Campbell Introduction 94(1) The Binary Multicommodity Flow Problem 95(1) Penalty Functions for discrete Problems 96(4) Simulated Annealing for Discrete Multicommodity Flows 100(3) Results 103(1) Conclusions 104(5) References 104(5) Part II NONSMOOTH OPTIMIZATION A Quadratic Recourse Function for the Two-Stage Stochastic Program 109(14) John R. Birge Stephen M. Pollock Liqun Qi Introduction 110(1) The Recourse Function 111(2) Differentiability of the Quadratic Recourse Function 113(2) Approximation to the Linear Recourse Function 115(5) Conclusions 120(3) References 120(3) Lagrange Multipliers for Nonconvex Optimization 123(6) B. D. Craven Introduction 124(1) Necessary Conditions 125(2) Sufficient Conditions 127(1) Duality 127(2) References 128(1) Class--Inclusion Properties for Convex Functions 129(6) Andrew Eberhard Charles E. M. Pearce Introduction 130(1) Proper Class Inclusions 131(1) Lower Semicontinuity 132(3) References 132(3) On Generic Locally Convex Vector Functions 135(18) V. Gershkovich B.D. Craven D. Ralph Introduction 136(1) Regular and Critical Points of Vector Functions 137(4) Generic LC Vector Functions F: Mn → IRk with 2k -- 4 < n 141(6) On Locally Convex Vector Functions with Small Singularities 147(3) Future Research 150(3) References 151(2) Essential Components and Connectedness of Solution Set for Complementarity Problems 153(14) George Isac George X.Z. Yuan Introduction 154(1) Preliminaries 154(1) Complementarity Problems 155(1) Connectedness of Solution Set 155(2) Essential Connected Components of Solution Set for Complementarity Problems 157(2) Applications to Complementarity Theory 159(2) The General Case 161(6) References 163(4) On Relations Between Vector Variational Inequality and Vector Optimization Problem 167(16) Gue Myung Lee Introduction 168(1) Minty Type Vector Variational Inequality 168(5) Weak Vector Variational Inequality 173(3) Existence Theorems for Vector Optimization Problem 176(7) References 178(5) Part III OPTIMIZATION METHODS Parameter Estimation in Dynamic Systems 183(22) Klaus Schittkowski Introduction 184(1) Data Fitting Methods 185(4) Systems of Ordinary Differential Equations 189(2) Systems of Differential Algebraic Equations 191(2) Systems of One-Dimensional Time-Dependent Partial Differential Equations 193(4) Systems of One-Dimensional Partial Differential Algebraic Equations 197(2) Applications 199(1) Conclusions 200(5) References 200(5) Methods of Feasible Directions: A Review 205(16) Xibin Chen Michael M. Kostreva Introduction 206(1) Typical Methods of Feasible Directions 207(7) The Comparisons of Three MFD 214(3) Concluding Remarks 217(4) References 218(3) Computational Method for a Class of Optimal Switching Control Problems 221(18) Y. Liu K.L. Teo Introduction 222(1) Problem Formulation 223(1) Problem Transformation 224(9) Gradient Formulae 233(1) Example 233(3) Conclusions 236(3) References 237(2) Optimization by Way of the Trajectory Following Method 239(16) Thomas L. Vincent Introduction 240(2) Trajectory Following Algorithm for Simple Constraints 242(2) Non-Simple Constraints 244(2) Linear/Quadratic Programming 246(3) Global Minimization 249(5) Conclusions 254(1) References 254(1) Solving Hamilton-Jacobi-Bellman Equations by an Upwind Finite Difference Method 255(14) S. Wang F. Gao K.L. Teo Introduction 257(1) The Method 258(2) Stability of the Scheme 260(4) Numerical Experiments 264(4) Conclusions 268(1) References 268(1) An Efficient Approximation Method for a Class of Continuous Linear Programs 269(18) K. H. Wong M. I. Kasiama C.Myburgh Introduction 270(1) Statement of the Problem 270(1) Approximate Problem 271(3) Analysis of the Method 274(2) Piecewise Linear Continuous Approximation 276(2) Constraint Approximation 278(2) Convergence Result 280(2) Example 282(5) References 284(3) Part IV APPLICATIONS Calibration of Parameters for a Combined Gravity and Traffic Assignment Model 287(18) Renlong Han Introduction 288(1) Proposed Model 289(3) Algorithms 292(1) Model Tests 293(3) Results 296(5) Conclusions 301(4) References 302(3) A Restricted Variation Argument to Derive Necessary Conditions for the Optimal Control of a Train 305(10) Phil Howlett Introduction 306(1) Formulation of A General Vehicle Control Problem with Discrete Control 306(1) Existence of An Optimal Strategy 307(1) The Equations of Motion for A Typical Train Control Problem 308(1) The Train Control Problem on Flat Track 309(1) The Restricted Variation Argument to Derive Necessary Conditions for Optimal Switching Times 310(5) References 313(2) Determination of Optimal Batch Size for a Manufacturing System 315(14) Ruhul Sarker Charles Newton Introduction 316(1) Problem Statement 316(2) Model Formulation 318(4) Solution Methodology 322(1) Results and Discussions 323(3) Conclusions 326(3) References 326(3) Parameter Estimation in a Mathematical Model for Substrate Diffusion in a Metabolically Active Cutaneous Tissue 329(1) Klaus Schittkowski Introduction 330(1) The Dynamical System 331(2) Solution Method 333(1) A Transdermal Diffusion Model 334(3) Numerical Results 337(2) Conclusions 339(2) References 341