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We focus on some convex separable optimization problems, considered by the author in previous papers, for which problems, necessary and sufficient conditions or sufficient conditions have been proved, and convergent algorithms of polynomial computational complexity have been proposed for solving these problems.The concepts ofwell-posedness of optimization problems in the sense of Tychonov,Hadamard, and in a generalized sense, as well as calmness in the sense of Clarke, are discussed. It is shown that the convex separable optimization problems under consideration are calm in the sense of Clarke. The concept of stability of the set of saddle points of the Lagrangian in the sense of Gol'shtein is also discussed, and it is shown that this set is not stable for the "classical" Lagrangian. However, it turns out that despite this instability, due to the specificity of the approach, suggested by the author for solving problems under consideration, it is not necessary to use modified Lagrangians but only the "classical" Lagrangians. Also, a primal-dual analysis for problems under consideration in view of methods for solving them is presented. [ABSTRACT FROM AUTHOR]

We consider the problem of projecting a point onto a region defined by a linear equality or inequality constraint and two-sided bounds on the variables. Such problems are interesting because they arise in various practical problems and as subproblems of gradient-type methods for constrained optimization. Polynomial algorithms are proposed for solving these problems and their convergence is proved. Some examples and results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

We consider the problem of minimizing a convex quadratic function over a region defined by a linear equality or inequality constraint and two-sided bounds on the variables (box constraints) in Rn. Such problems are interesting from both theoretical and practical points of view because they arise as subproblems of some mathematical programming problems as well as in various practical problems. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented. [ABSTRACT FROM AUTHOR]

Hydrogen sulfide is frequently met in natural waters, like mineral springs, but mostly it is found in marine water with low renewal rate. The Black Sea has extremely high hydrogen sulfide content. It can be utilized in different ways, but the most promising one is direct conversion into electricity. This result can be attained by a sulfide-driven fuel cell (SDFC), converting sulfide to sulfate thus releasing electric energy up to 24 GJ/t. One of the most important problems is the mass transfer limitation on oxygen transfer in the cathode space of the fuel cell. This problem can be solved using a gas diffusion electrode or highly efficient saturation by oxygen in an ejector of the Venturi tube type. This work presents experimental data in laboratory-scale SDFC for sulfide conversion into sulfate, sulfite and polysulfide releasing different amounts of electric energy. Two types of aeration are tested: direct air blow and Venturi-tube ejector. Besides pure graphite, two catalysts, i.e., cobalt spinel and zirconia-doped graphite were tested as anodes. Experiments were carried out at initial sulfide concentrations from 50 to 300 mg/L. Sulfate, sulfite and thiosulfate ions were detected in the outlet solutions from the fuel cell. The electrochemical results show good agreement with the chemical analyses. Most of the results show attained high efficiencies of the fuel cell, i.e., up to 80%. The practical applications of this method can be extended for other purposes, like treatment of polluted water together with utilization as energy. [ABSTRACT FROM AUTHOR]

We consider the problem of minimizing a convex linear-fractional separable function over a feasible region defined by a convex inequality constraint or linear inequality constraint, and bounds on the variables (box constraints). These problems are interesting from both theoretical and practical points of view because they arise in some mathematical programming problems and in various practical problems. Polynomial algorithms for solving such problems are proposed and their convergence is proved. Some examples and results of numerical experiments are also presented. [ABSTRACT FROM PUBLISHER]