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Effect of mangrove forest structures on wave attenuation in coastal Vietnam

Bao T.Q.

Oceanologia

2011

No. 53 (3)

807-818

This paper analyses wave attenuation in coastal mangrove forests in Vietnam. Data from 32 mangrove plots of six species located in 2 coastal regions are used for this study. In each plot, mangrove forest structures and wave height at different cross-shore distances are measured. Wave height closely relates to cross-shore distances. 92 exponential regression equations are highly significant with R2 > 0.95 and P val. < 0.001. Wave height reduction depends on initial wave height, cross-shore distances, and mangrove forest structures. This relationship is used to define minimum mangrove band width for coastal protection from waves in Vietnam.

Variational principles for set-valued mappings with applications to multiobjective optimization

Bao T. Q., Mordukhovich B. S.

Control and Cybernetics

2007

Vol. 36, no 3

531-562

This paper primarily concerns the study of general classes of constrained multiobjective optimization problems (including those described via set-valued and vector-valued cost mappings) from the viewpoint of modern variational analysis and generalized differentiation. To proceed, we first establish two variational principles for set-valued mappings, which-being certainly of independent interest-are mainly motivated by applications to multiobjective optimization problems considered in this paper. The first variational principle is a set-valued counterpart of the seminal derivative-free Ekeland variational principle, while the second one is a set-valued extension of the subdifferential principle by Mordukhovich and Wang, formulated via an appropriate subdifferential notion for set-valued mappings with values in partially ordered spaces. Based on these variational principles and corresponding tools of generalized differentiation, we derive new conditions of the coercivity and Palais-Smale types ensuring the existence of optimal solutions to set-valued optimization problems with noncompact feasible sets in infinite dimensions and then obtain necessary optimality and suboptimality conditions for nonsmooth multiobjective optimization problems with general constraints, which are new in both finite-dimensional and infinite-dimensional settings.