Semi-infinite programming and applications : an international symposium, Austin, Texas, September 8-10, 1981

I Duality Theory.- Ascent Ray Theorems and Some Applications.- 1. Introduction.- 2. Application to Semi-Infinite Programming.- 3. Intersections of Convex Sets.- 4. Convex Optimization Application.- 5. What About Systems With Infinitely Many Variables?.- References.- Semi-Infinite Programming Duality: How Special Is It?.- 1. Introduction.- 2. Direct Techniques: (I) Primal Reduction Theorems.- 3. Direct Techniques: (II) Dual Reduction Theorems.- 4. Abstract Linear Duality.- 5. Specializations.- 6. Abstract Convex and Differentiable Programming.- 7. Nonsmooth Techniques.- 8. Conclusion.- References.- A Saddle Value Characterization of Fan's Equilibrium Points.- 1. Introduction: A Biextremal Formulation.- 2. A Separably-Infinite, Biextremal Formulation of the Fan Equilibrium Problem.- 3. Equivalent Dual Pair of Separably-Infinite Programs.- 4. The Fan Equilibrium as the Unique Zero of VM(?).- 5. The Fan Equilibrium Value as Saddle Value of a Ratio Game.- 6. Conclusion.- References.- Duality in Semi-Infinite Linear Programming.- 1. Introduction.- 2. The Homogeneous Case.- 3. The Inhomogeneous Case and Duality Results.- References.- On the Role of Duality in the Theory of Moments.- 1. Introduction.- 2. A General Moment Problem.- 3. The Finite Case.- 4. A General Result.- 5. A General Transportation Problem.- 6. Theorems of Kantorovich, Rubinstein, Nachbin, and Strassen.- 7. Transshipment.- 8. Appendix.- References.- Existence Theorems in Semi-Infinite Programs.- 1. Introduction with Problem Setting.- 2. Existence Theorems for NSIP.- 3. Semi-Infinite Quadratic Program.- References.- II Algorithmic Developments.- An Algorithm for a Continuous Version of the Assignment Problem.- 1. The Continuous Transportation Problem.- 2. Basic Solutions and Assignments.- 3. The Continuous Assignment Problem and Its Algorithm.- References.- Numerical Estimation of Optima by Use of Duality Inequalities.- 1. Introduction.- 2. Minima of Functions of One Variable.- 3. Minima of Functions of Two Variables.- 4. The Apex Program.- 5. The Question of a Duality Gap.- 6. Estimating the Coordinates of an Optimum Point.- 7. Estimating Constrained Minima.- 8. Discussion.- References.- Globalization of Locally Convergent Algorithms for Nonlinear Optimization Problems with Constraints.- 1. Introduction.- 2.1. Local Stability Sets, Critical Points.- 2.2. Convergence of Local Methods on Local Stability Sets.- 2.3. Determination of Critical Points.- 2.4. Determination of the New Active Index Set.- 3. A Concept of a Globally Convergent Algorithm.- 4. A Concrete Imbedding for Convex Optimization Problems.- References.- A Three-Phase Algorithm for Semi-Infinite Programs.- 1. Introduction.- 2. Semi-Infinite Programs of P-type.- 3. Semi-Infinite Programs of D-type.- 4. Necessary Condition for Optimality.- 5. Approximation of Programs (P) and (D) with Discretized Problems.- 6. A General Three-Phase Algorithm.- References.- A Review of Numerical Methods for Semi-Infinite Optimization.- 1. Introduction.- 2. Exchange Methods.- 3. Linear Semi-Infinite and Differentiable Convex Programming.- 4. The Relation of Exchange Methods to Cutting Plane Methods.- 5. The Case of a Strongly Unique Solution.- 6. A Discretization Method.- 7. Local Reduction to a Finite Convex Problem.- 8. Some Examples of Methods for Solving the Reduced Problem.- 9. Some Remarks on the Nonlinear Case.- References.- An Algorithm for Minimizing Polyhedral Convex Functions.- 1. Introduction.- 2. A Continuation Procedure.- 3. Treatment of Degeneracy.- 4. Points Relating to Computation.- References.- Numerical Experiments with Globally Convergent Methods for Semi-Infinite Programming Problems.- 1. Introduction.- 2. A Model Algorithm.- 3. An Implementation of the Algorithm.- 4. Numerical Results.- 5. A Modified Subproblem.- 6. Concluding Remarks.- References.- III Problem Analysis and Modeling.- On the Partial Construction of the Semi-Infinite Banzhaf Polyhedron.- 1. Introduction.- 2. The Semi-Infinite Problem.- 3. Properties of the Semi-Infinite Polyhedron.- 4. Optimization.- References.- Semi-Infinite and Fuzzy Set Programming.- 1. Introduction.- 2. C/C Semi-Infinite Linear Programs.- 3. Fuzzy Set Programming.- 4. Relationship with C/C Semi-Infinite Programs.- References.- Semi-Infinite Optimization in Engineering Design.- 1. Introduction.- 2. Formulation of Engineering Design Problems in SIP Form.- 2.1. Seismic Resistant Design of Structures.- 2.2. Design of SISO Control Systems.- 2.3. Design of MIMO Control Systems.- 2.4. Electronic Circuit Design.- 3. SIP Algorithms for Engineering Design.- 4. Conclusion.- References.- A Moment Inequality and Monotonicity of an Algorithm.- 1. Introduction.- 2. A Problem.- 3. Examples.- 4. Sufficient Conditions for Optimality - Two Alternative Forms.- 5. Algorithms.- 6. A First or Intermediate Phase Algorithm.- 7. Moment Lemma and a Sufficient Condition.- 8. Empirical Information.- References.- IV Optimality Conditions and Variational Principles.- Second Order Conditions in Nonlinear Nonsmooth Problems of Semi-Infinite Programming.- 1. Introduction.- 2. Statements of Main Results.- 3. An Auxiliary Problem.- 4. Proofs of Main Theorems.- References.- On Stochastic Control Problems with Impulse Cost Vanishing.- 1. Introduction.- 2. Assumptions and Notations.- 3. Stochastic Impulse Control Problem.- 3.1. The General Case.- 3.2. A Particular Case.- 4. Existence of An Optimal Impulse Control.- References.- Dual Variational Principles in Mechanics and Physics.- 1. Description of the Primal Problem - Examples.- 2. Dual Problem.- 3. Relaxed Problem and Extension of Duality.- References.- Authors, Participants, and Affiliations.- Referees.- Table of Contents of the Book of Abstracts.