Theory of Linear Optimization

Finite systems of linear inequalities basic definitions the structure of polyhedrons bounded polyhedrons a parametric representation of polyhedrons the Farkas-Minowski theorem on dependent inequalities attainability theorem for inequalities-implications of second kind a refined formulation of the Farkas-Minowski theorem conditions of compatibility of a finite system of linear inequalities the cleaning theorem separability of nonintersecting polyhedrons the Fourier elimination method linear programming setting of the problem of linear programming and some of its properties economic interpretation of the linear programming problem duality - informative approach the duality theorem the optimality conditions informative interpretations of optimality conditions matrix plays and duality the theorem of marginal values the method of exact penalty functions in linear programming LP problems with several criterion functions inconsistent problems of linear programming classification of improper problems of linear programming (IP LP) informative interpretation of improper problems of linear programming methods of correction of improper problems of linear programming - general approach duality - the main theorem special realizations of duality the duality problem for l-problems problems of successive linear programming and duality the scheme of duality formation in linear successive programming solvability conditions for lexicographic optimisation problems the duality theorem reduction of lexicographic optimisation problems to systems of linear inequalities lexicographic duality for improper LP problems - a special case duality for improper LP problems in lexicographic interpretation symmetric duality for the Pareto optimisation problem stability and well-posedness of linear programming problems necessary definitions and auxiliary results stability of the linear programming problem well-posedness of linear programming problems the Tikhonov regularization of linear programming problems methods of projection in linear programming Fejer mappings and their properties basic constructions of Fejer mappings for algebraic polyhedrons decomposition and parallelizing of Fejer processes randomization of Fejer processes Fejer processes and inconsistent systems of linear inequalities Fejer processes for regularized LP problems piecewise linear functions and problems of disjunctive programming introductory considerationss-extensions of linear functional space. (Part contents).