Suggested research topics in sensitivity and stability analysis for semi-infinite programming problems

We suggest several important research topics for semi-infinite programs whose problem functions and index sets contain parameters that are subject to perturbation. These include optimal value and optimal solution sensitivity and stability properties and penalty function approximation techniques. The approaches proposed are a natural carryover from parametric nonlinear programming, with emphasis on practical applicability and computability.

[1]  T. Pietrzykowski The potential method for conditional maxima in the locally compact metric spaces , 1970 .

[2]  G. A. Watson,et al.  Lagrangian Methods for Semi-Infinite Programming Problems , 1985 .

[3]  M. Fukushima,et al.  A comparative study of several semi-infinite nonlinear programming algorithms , 1988 .

[4]  H. Maurer,et al.  Differential stability in infinite-dimensional nonlinear programming , 1980 .

[5]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, STOC '84.

[6]  Kenneth O. Kortanek,et al.  Numerical treatment of a class of semi‐infinite programming problems , 1973 .

[7]  Marc Teboulle,et al.  Second order necessary optimality conditions for semi-infinite programming problems , 1979 .

[8]  B. Brosowski,et al.  Parametric Optimization and Approximation , 1985 .

[9]  Günther Nürnberger,et al.  Unicity in Semi-Infinite Optimization , 1984 .

[10]  J. M. Borwein,et al.  Direct theorems in semi-infinite convex programming , 1981, Math. Program..

[11]  Nicholas I. M. Gould,et al.  An exact penalty function for semi-infinite programming , 1987, Math. Program..

[12]  E. Polak,et al.  Unified steerable phase I-phase II method of feasible directions for semi-infinite optimization , 1991 .

[13]  Michael C. Ferris,et al.  An interior point algorithm for semi-infinite linear programming , 1989, Math. Program..

[14]  Anthony V. Fiacco,et al.  Sensitivity analysis for nonlinear programming using penalty methods , 1976, Math. Program..

[15]  R. Rockafellar Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming , 1982 .

[16]  Jean-Paul Penot,et al.  Differentiability of Relations and Differential Stability of Perturbed Optimization Problems , 1984 .

[17]  R. P. Hettich,et al.  Semi-infinite programming: Conditions of optimality and applications , 1978 .

[18]  Sven-Åke Gustafson,et al.  On the Computational Solution of a Class of Generalized Moment Problems , 1970 .

[19]  Rainer Hettich,et al.  Numerische Methoden der Approximation und semi-infiniten Optimierung , 1982 .

[20]  E. Anderson,et al.  Linear programming in infinite-dimensional spaces : theory and applications , 1987 .

[21]  Joachim Piehler Einführung in die lineare Optimierung , 1966 .

[22]  J. Borwein SEMI-INFINITE PROGRAMMING DUALITY: HOW SPECIAL IS IT? , 1983 .

[23]  R. Tichatschke,et al.  A cutting-plane method for quadratic semi infinite programming problems , 1988 .

[24]  Sven-Åke Gustafson NONLINEAR SYSTEMS IN SEMI-INFINITE PROGRAMMING , 1973 .

[25]  E. Polak,et al.  A recursive quadratic programming algorithm for semi-infinite optimization problems , 1982 .

[26]  G. Alistair Watson,et al.  A projected lagrangian algorithm for semi-infinite programming , 1985, Math. Program..

[27]  S. Gustafson A Three-Phase Algorithm for Semi-Infinite Programs , 1983 .

[28]  M. Fukushima,et al.  Implementable L ∞ penalty-function method for semi-infinite optimization , 1987 .

[29]  Rainer Hettich,et al.  A Review of Numerical Methods for Semi-Infinite Optimization , 1983 .

[30]  A. D. Ioffe Second Order Conditions in Nonlinear Nonsmooth Problems of Semi-Infinite Programming , 1983 .

[31]  Sven-Åke Gustafson,et al.  Investigating semi-infinite programs using penalty functions and Lagrangian methods , 1986, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[32]  E. Polak Semi-Infinite Optimization in Engineering Design , 1983 .

[33]  Michael A. Saunders,et al.  On projected newton barrier methods for linear programming and an equivalence to Karmarkar’s projective method , 1986, Math. Program..

[34]  R. Hettich,et al.  Two case-studies in parametric semi-infinite programming , 1985 .

[35]  J. Flachs Sensitivity Analysis in Generalized Rational Approximation with Restricted Denominator , 1984 .

[36]  On Parametric Infinite Optimization , 1984 .

[37]  A. Fiacco,et al.  Convexity and concavity properties of the optimal value function in parametric nonlinear programming , 1983 .

[38]  Rainer Hettich,et al.  An implementation of a discretization method for semi-infinite programming , 1986, Math. Program..

[39]  F. Clarke Generalized gradients and applications , 1975 .

[40]  Alexander Shapiro,et al.  Second-Order Derivatives of Extremal-Value Functions and Optimality Conditions for Semi-Infinite Programs , 1985, Math. Oper. Res..

[41]  Abraham Charnes,et al.  A duality theory for convex programs with convex constraints , 1962 .

[42]  James Renegar,et al.  A polynomial-time algorithm, based on Newton's method, for linear programming , 1988, Math. Program..

[43]  Anthony V. Fiacco,et al.  Computable bounds on parametric solutions of convex problems , 1988, Math. Program..

[44]  K. R. Gehner,et al.  Necessary and Sufficient Optimality Conditions for the Fritz John Problem with Linear Equality Constraints , 1974 .

[45]  G. A. Watson,et al.  Numerical Experiments with Globally Convergent Methods for Semi-Infinite Programming Problems , 1983 .

[46]  C. Dunham Dependence of Best Rational Chebyshev Approximations on the Domain , 1977, Canadian Mathematical Bulletin.

[47]  N. Megiddo Pathways to the optimal set in linear programming , 1989 .

[48]  Kenneth O. Kortanek,et al.  Semi-Infinite Programming and Applications , 1983, ISMP.

[49]  J. E. Falk,et al.  Infinitely constrained optimization problems , 1976 .

[50]  Bruno Brosowski,et al.  Parametric semi-infinite optimization , 1982 .

[51]  A. Fiacco,et al.  Exact Sensitivity Analysis Using Augmented Lagrangians. , 1977 .

[52]  E. Polak On the mathematical foundations of nondifferentiable optimization in engineering design , 1987 .

[53]  Rainer Hettich,et al.  Directional derivatives for the value-function in semi-infinite programming , 1989, Math. Program..

[54]  W. Wetterling,et al.  Definitheitsbedingungen für relative Extrema bei Optimierungs- und Approximationsaufgaben , 1970 .