We provide an improvement of the maximum principle of Pontryagin of the Optimal Control problems. We establish differentiability properties of the value function of problems of Optimal Control with assumptions as low as possible. Notably, we lighten the assumptions by using Gâteaux and Hadamard differentials.
Background: Malaria remains a global challenge with approximately 228 million cases and 405,000 malaria-related deaths reported in 2018 alone; 93% of which were in sub-Saharan Africa. Aware of the critical role than environmental factors play in malaria transmission, this study aimed at assessing the relationship between precipitation, temperature, and clinical malaria cases in East Africa and how the relationship may change under 1.5 o C and 2.0 o C global warming levels (hereinafter GWL1.5 and GWL2.0, respectively). Methods: A correlation analysis was done to establish the current relationship between annual precipitation, mean temperature, and clinical malaria cases. Differences between annual precipitation and mean temperature value projections for periods 2008-2037 and 2023-2052 (corresponding to GWL1.5 and GWL2.0, respectively), relative to the control period (1977-2005), were computed to determine how malaria transmission may change under the two global warming scenarios. Results : A predominantly positive/negative correlation between clinical malaria cases and temperature/precipitation was observed. Relative to the control period, no major significant changes in precipitation were shown in both warming scenarios. However, an increase in temperature of between 0.5 o C and 1.5 o C and 1.0 o C to 2.0 o C under GWL1.5 and GWL2.0, respectively, was recorded. Hence, more areas in East Africa are likely to be exposed to temperature thresholds favourable for increased malaria vector abundance and, hence, potentially intensify malaria transmission in the region. Conclusions : GWL1.5 and GWL2.0 scenarios are likely to intensify malaria transmission in East Africa. Ongoing interventions should, therefore, be intensified to sustain the gains made towards malaria elimination in East Africa in a warming climate.
The bin-packing problem continues to remain relevant in numerous application areas. This technical report discusses the empirical performance of different bin-packing heuristics for certain test problems.
Starting from a symmetrization and extension of the basic definitions and results of dissipativity theory we obtain new results on cyclo-dissipativity; in particular their external characterization and description of the set of storage functions.
Motivated by the fact that not all nonconvex optimization problems are difficult to solve, we survey in this paper three widely-used ways to reveal the hidden convex structure for different classes of nonconvex optimization problems. Finally, ten open problems are raised.
We define Walrasian economic equilibrium in convex regions. We introduce the definition of strict-proper quasimonotone functions, and derive some necessary and sufficient conditions for the existence and uniqueness of Walrasian equilibrium vectors in convex regions.
In this paper provide sufficient and necessary conditions for the minimax equality for extended-valued $Φ$-convex functions. As an application we establish sufficient and necessary conditions for the minimax equality for convex-concave functions.
We review in a unified way results for two types of stochastic chemical reaction systems for which moments can be effectively computed: feedforward networks and complex-balanced networks.
We discuss final-offer arbitration where two quantitative issues are in dispute and model it as a zero-sum game. Under reasonable assumptions we both derive a pure strategy pair and show that it is both a local equilibrium and furthermore that it is the unique global equilibrium.
The paper considers an extension of factor analysis to moving average processes. The problem is formulated as a rank minimization of a suitable spectral density. It is shown that it can be adequately approximated via a trace norm convex relaxation.
The backward-backward algorithm is a tool for finding minima of a regularization of the sum of two convex functions in Hilbert spaces. We generalize this setting to Hadamard spaces and prove the convergence of an error-tolerant version of the backward-backward method.
We give an elementary proof of a somewhat curious result, namely, that deciding whether a convex function is self-concordant is in general an intractable problem.
Using a definition of ASF sequences derived from the definition of asymptotic contractions of the final type of ACF, we give some new fixed points theorem for cyclic mappings and alternating mapping which extend results from T.Suzuki and X.Zhang.