Adjusting Dual Iterates in the Presence of Critical Lagrange Multipliers
08 Jun 2020-Siam Journal on Optimization (Society for Industrial and Applied Mathematics)-Vol. 30, Iss: 2, pp 1555-1581
TL;DR: It is a well-known phenomenon that the presence of critical Lagrange multipliers in constrained optimization problems may cause a deterioration of the convergence speed of primal-dual Newton-type mappings.
Abstract: It is a well-known phenomenon that the presence of critical Lagrange multipliers in constrained optimization problems may cause a deterioration of the convergence speed of primal-dual Newton-type m...
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TL;DR: In this article, the authors considered the case when there exist critical Lagrange multipliers, and provided a basis for application of known acceleration techniques, such as extrapolation, and allowed the formulation of algorithms that can outperform the standard SQP with BFGS approximations of the Hessian on problems with degenerate constraints.
Abstract: This paper concerns the issue of asymptotic acceptance of the true Hessian and the full step by the sequential quadratic programming algorithm for equality-constrained optimization problems. In order to enforce global convergence, the algorithm is equipped with a standard Armijo linesearch procedure for a nonsmooth exact penalty function. The specificity of considerations here is that the standard assumptions for local superlinear convergence of the method may be violated. The analysis focuses on the case when there exist critical Lagrange multipliers, and does not require regularity assumptions on the constraints or satisfaction of second-order sufficient optimality conditions. The results provide a basis for application of known acceleration techniques, such as extrapolation, and allow the formulation of algorithms that can outperform the standard SQP with BFGS approximations of the Hessian on problems with degenerate constraints. This claim is confirmed by some numerical experiments.
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TL;DR: In this article , the authors developed a mathematical model to justify the need to use radiation and chemical protection services as part of specialized fire and rescue units in the subjects of the Russian Federation.
Abstract: Introduction. Recently, much attention has been paid to the issues of long-term development of specialized fire and rescue units of the Federal Fire Service of the State Fire Service. In this regard, there is a need to develop criteria to justify the use of a particular service as part of specialized fire and rescue units. Therefore, the objective of this study is to develop a mathematical model to justify the need to use radiation and chemical protection services as part of specialized fire and rescue units in the subjects of the Russian Federation.Materials and Methods. Justification of the need to use radiation and chemical protection services as part of specialized fire and rescue units has been carried out using the theory of fuzzy sets. The mathematical model takes into account the climatic and geographical features of the subjects, indicators of social, technical and economic development, and the risks of emergencies and fires. It also takes into account the availability of forces and means of a Unified State system for the prevention and liquidation of emergency situations in each subject of the Russian Federation. In total, 15 indicators were selected that characterize the need to use radiation and chemical protection services as part of specialized fire and rescue units. A desirability function is defined for each indicator, which shows which values of the indicator are the most acceptable from the point of view of the need to use radiation and chemical protection services as part of specialized fire and rescue units.Results. Using the developed model, the subjects of the Russian Federation are identified in which the need for radiation and chemical protection service as part of specialized fire and rescue units is the highest. It is proposed to create a radiation and chemical protection service of the 1st category in the Moscow, Sverdlovsk and Rostov regions, in the Krasnoyarsk and Primorsky Territories and in St. Petersburg. In 21 subjects it is proposed to use the radiation and chemical protection service of the 2nd category. In other subjects, it is proposed to assign the 3rd category to the radiation and chemical protection service.Discussion and Conclusion. The mathematical model developed using the theory of fuzzy sets will allow a more differentiated approach to the creation of a radiation and chemical protection service as part of specialized fire and rescue units and increase the efficiency of the functioning of this service and specialized fire and rescue units as a whole. The presented model can be applied to justify the need to use other services and groups as part of specialized fire and rescue units.
References
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376 citations
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176 citations