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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 42 (1984), S. 467-485 
    ISSN: 1573-2878
    Keywords: Optimal control ; hyperbolic partial differential equations ; Darboux boundary conditions ; strong variational algorithm ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems involving linear hyperbolic partial differential equations with Darboux boundary conditions. A strong variational algorithm has been obtained for solving this class of optimal control problems in a previous paper by the third and the first authors. It was also shown that anyL ∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that the control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problems.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 44 (1984), S. 509-526 
    ISSN: 1573-2878
    Keywords: Control parameterization ; piecewise constant functions ; linear time-lag systems ; linear terminal constraints ; computational schemes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving linear hereditary systems with bounded control region and linear terminal constraints. Several examples have been solved to illustrate the efficiency of the technique.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 46 (1985), S. 295-317 
    ISSN: 1573-2878
    Keywords: Nonlinear time-lag systems ; linear control constraints ; nonlinear terminal inequality constraints ; conditional gradient methods ; feasible direction methods ; control parametrization ; initial feasible control ; computational schemes ; finite convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A computational algorithm for a class of time-lag optimal control problems involving control and terminal inequality constraints is presented. The convergence properties of the algorithm is also investigated. To test the algorithm, an example is solved.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 47 (1985), S. 91-107 
    ISSN: 1573-2878
    Keywords: Control parameterization ; piecewise constant functions ; nonlinear hereditary systems ; linear control constraints ; computational schemes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a computational scheme using the technique of control parameterization is developed for solving a class of optimal control problems involving nonlinear hereditary systems with linear control constraints. Several examples have been solved to test the efficiency of the technique.
    Type of Medium: Electronic Resource
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  • 5
    Publication Date: 2024-02-07
    Description: The abundance and size distribution of marine particles control a range of biogeochemical and ecological processes in the ocean, including carbon sequestration. These quantities are the result of complex physical-biological interactions that are difficult to observe, and their spatial and temporal patterns remain uncertain. Here, we present a novel analysis of particle size distributions (PSDs) from a global compilation of in situ Underwater Vision Profiler 5 (UVP5) optical measurements. Using a machine learning algorithm, we extrapolate sparse UVP5 observations to the global ocean from well-sampled oceanographic variables. We reconstruct global maps of PSD parameters (biovolume [BV] and slope) for particles at the base of the euphotic zone. These reconstructions reveal consistent global patterns, with high chlorophyll regions generally characterized by high particle BV and flatter PSD slope, that is, a high relative abundance of large versus small particles. The resulting negative correlations between particle BV and slope further suggests synergistic effects on size-dependent processes such as sinking particle fluxes. Our approach and estimates provide a baseline for an improved understanding of particle cycles in the ocean, and pave the way to global, three-dimensional reconstructions of PSD and sinking particle fluxes from the growing body of UVP5 observations.
    Type: Article , PeerReviewed
    Format: text
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  • 6
    Publication Date: 2024-02-07
    Description: Export of sinking particles from the surface ocean is critical for carbon sequestration and to provide energy to the deep biosphere. The magnitude and spatial patterns of this export have been estimated in the past by in situ particle flux observations, satellite-based algorithms, and ocean biogeochemical models; however, these estimates remain uncertain. Here, we use a recent machine learning reconstruction of global ocean particle size distributions (PSDs) from Underwater Vision Profiler 5 measurements to estimate carbon fluxes by sinking particles (35 μm–5 mm equivalent spherical diameter) from the surface ocean. We combine global maps of PSD properties with empirical relationships constrained against in situ flux observations to calculate particulate carbon export from the euphotic zone (5.8 ± 0.1 Pg C y−1) and annual maximum mixed layer depths (6.1 ± 0.1 Pg C y−1). The new flux reconstructions suggest a less variable seasonal cycle in the tropical ocean and a more persistent export in the Southern Ocean than previously recognized. Smaller particles (less than 418 μm) contribute most of the flux globally, while larger particles become more important at high latitudes and in tropical upwelling regions. Export from the annual maximum mixed layer exceeds that from the euphotic zone over most of the low-latitude ocean, suggesting shallow particle recycling and net heterotrophy in the deep euphotic zone. These estimates open the way to fully three-dimensional global reconstructions of particle fluxes in the ocean, supported by the growing database of in situ optical observations.
    Type: Article , PeerReviewed , info:eu-repo/semantics/article
    Format: text
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