Semi-Infinite Programming by Miguel A. Goberna, Marco A. López (auth.), Rembert Reemtsen,

By Miguel A. Goberna, Marco A. López (auth.), Rembert Reemtsen, Jan-J. Rückmann (eds.)

Semi-infinite programming (briefly: SIP) is a thrilling a part of mathematical programming. SIP difficulties comprise finitely many variables and, unlike finite optimization difficulties, infinitely many inequality constraints. Prob­ lems of this sort certainly come up in approximation concept, optimum regulate, and at a variety of engineering functions the place the version includes not less than one inequality constraint for every price of a parameter and the parameter, repre­ senting time, area, frequency etc., varies in a given area. The remedy of such difficulties calls for specific theoretical and numerical suggestions. the idea in SIP in addition to the variety of numerical SIP tools and appli­ cations have increased very quickly over the past years. as a result, the most target of this monograph is to supply a set of educational and survey variety articles which symbolize a considerable a part of the modern physique of data in SIP. we're happy that best researchers have contributed to this quantity and that their articles are protecting a variety of very important subject matters during this topic. it's our wish that either skilled scholars and scientists might be good steered to refer to this quantity. We received the assumption for this quantity once we have been organizing the semi-infinite seasoned­ gramming workshop which used to be held in Cottbus, Germany, in September 1996.

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M. Strojwas. On constraint sets of infinite linear programs over ordered fields. Math. Programming, 33:146-61, 1985. [47] M. A. Lopez and E. Vercher. Optimality conditions for nondifferentiable convex semi-infinite programming. Math. Programming, 27:307-19, 1983. [48] E. Marchi, R. Puente, and V. N. Vera de Serio. Quasi-polyhedral sets in semiinfinite linear inequality systems. , 255:157-69, 1997. [49] M. J. D. Powell. Karmarkar's algorithm: A view from non-linear programming. IMA Bulletin, 26:165-81, 1990.

Goberna, M. A. Lopez, J. A. Mira, and J. Valls. On the existence of solutions for linear inequality systems. J. Math. Anal. , 192:133-50, 1995. [33J M. A. Goberna, M. A. Lopez, and M. I. Todorov. Unicity in linear optimization. J. Opt. Th. , 86:37-56, 1995. [34J M. A. Goberna, M. A. Lopez, and M. I. Todorov. Stability theory for linear inequality systems, SIAM J. Matrix Anal. , 17:730-743, 1996. [35J M. A. Goberna, M. A. Lopez, and M. I. Todorov. Stability theory for linear inequality systems II: upper semicontinuity of the solution set mapping.

G. ). In [18, 55J corresponding stability results for noncompact feasible sets are established, where the lack of compactness is substituted by considering stability properties of certain compact subsets of M[h, gJ. An extension to feasible sets which depend on an additional real parameter is performed in [26J. Assuming (EMFCQ) and an appropriate generalization of the Condition C in [45J the stability of the feasible set is shown with respect to both perturbations of the function vector in the C;-topology and variations of the additional parameter.

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