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Ho Chi Minh City, Vietnam

Dinh N.,Vietnam National University, Ho Chi Minh City | Mordukhovich B.,Wayne State University | Nghia T.T.A.,Wayne State University | Nghia T.T.A.,Ho Chi Minh City University of Pedagogy
Mathematical Programming

The paper concerns the study of new classes of parametric optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain, among other constraints, infinitely many inequality constraints. These problems reduce to semi-infinite programs in the case of finite-dimensional spaces of decision variables. We focus on DC infinite programs with objectives given as the difference of convex functions subject to convex inequality constraints. The main results establish efficient upper estimates of certain subdifferentials of (intrinsically nonsmooth) value functions in DC infinite programs based on advanced tools of variational analysis and generalized differentiation. The value/marginal functions and their subdifferential estimates play a crucial role in many aspects of parametric optimization including well-posedness and sensitivity. In this paper we apply the obtained subdifferential estimates to establishing verifiable conditions for the local Lipschitz continuity of the value functions and deriving necessary optimality conditions in parametric DC infinite programs and their remarkable specifications. Finally, we employ the value function approach and the established subdifferential estimates to the study of bilevel finite and infinite programs with convex data on both lower and upper level of hierarchical optimization. The results obtained in the paper are new not only for the classes of infinite programs under consideration but also for their semi-infinite counterparts. © 2009 Springer and Mathematical Programming Society. Source

Devito R.P.,Michigan State University | Khoa D.T.,Institute for Nuclear Science and Technique | Austin S.M.,Michigan State University | Berg U.E.P.,Michigan State University | And 2 more authors.
Physical Review C - Nuclear Physics

Background: Analysis of data involving nuclei far from stability often requires the optical potential (OP) for neutron scattering. Because neutron data are seldom available, whereas proton scattering data are more abundant, it is useful to have estimates of the difference of the neutron and proton optical potentials. This information is contained in the isospin dependence of the nucleon OP. Here we attempt to provide it for the nucleon-208Pb system. Purpose: The goal of this paper is to obtain accurate n+208Pb scattering data and use it, together with existing p+208Pb and 208Pb (p,n)208BiIAS* data, to obtain an accurate estimate of the isospin dependence of the nucleon OP at energies in the 30-60-MeV range. Method: Cross sections for n+208Pb scattering were measured at 30.4 and 40.0 MeV, with a typical relative (normalization) accuracy of 2-4% (3%). An angular range of 15 to 130 was covered using the beam-swinger time-of-flight system at Michigan State University. These data were analyzed by a consistent optical-model study of the neutron data and of elastic p+208Pb scattering at 45 and 54 MeV. These results were combined with a coupled-channel analysis of the 208Pb(p,n) reaction at 45 MeV, exciting the 0 + isobaric analog state (IAS) in 208Bi. Results: The new data and analysis give an accurate estimate of the isospin impurity of the nucleon-208Pb OP at 30.4 MeV caused by the Coulomb correction to the proton OP. The corrections to the real proton OP given by the CH89 global systematics were found to be only a few percent, whereas for the imaginary potential it was greater than 20% at the nuclear surface. On the basis of the analysis of the measured elastic n+208Pb data at 40 MeV, a Coulomb correction of similar strength and shape was also predicted for the p+208Pb OP at energies around 54 MeV. Conclusions: Accurate neutron scattering data can be used in combination with proton scattering data and (p,n) charge exchange data leading to the IAS to obtain reliable estimates of the isospin impurity of the nucleon OP. © 2012 American Physical Society. Source

Loan D.T.,Institute for Nuclear Science and Technology | Loc B.M.,Ho Chi Minh City University of Pedagogy | Khoa D.T.,Institute for Nuclear Science and Technology
Physical Review C - Nuclear Physics

The nucleon mean-field potential has been thoroughly investigated in an extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3 and CDM3Y6 density dependent versions of the M3Y interaction. The single-particle (SP) energies of nucleons in NM are determined according to the Hugenholtz-Van Hove theorem, which gives rise naturally to a rearrangement term (RT) of the SP potential at the Fermi momentum. Using the RT obtained exactly at the different NM densities and neutron-proton asymmetries, a consistent method is suggested to take into account effectively the momentum dependence of the RT of the SP potential within the standard HF scheme. To obtain a realistic momentum dependence of the nucleon optical potential (OP), the high-momentum part of the SP potential was accurately readjusted to reproduce the observed energy dependence of the nucleon OP over a wide range of energies. The impact of the RT and momentum dependence of the SP potential on the density dependence of the nuclear symmetry energy and nucleon effective mass has been studied in detail. The high-momentum tail of the SP potential was found to have a sizable effect on the slope of the symmetry energy and the neutron-proton effective mass splitting at supranuclear densities of the NM. Based on a local density approximation, the folding model of the nucleon OP of finite nuclei has been extended to take into account consistently the RT and momentum dependence of the nucleon OP in the same mean-field manner, and successfully applied to study the elastic neutron scattering on the lead target at the energies around the Fermi energy. © 2015 American Physical Society. Source

Khanh P.D.,Ho Chi Minh City University of Pedagogy | Vuong P.T.,University of Technical Education
Journal of Global Optimization

A modified projection method for strongly pseudomonotone variational inequalities is considered. Strong convergence and error estimates for the sequences generated by this method are studied in two versions of the method: the stepsizes are chosen arbitrarily from a given fixed closed interval and the stepsizes form a non-summable decreasing sequence of positive real numbers. We also propose some interesting examples to analyze the obtained results. © 2013 Springer Science+Business Media New York. Source

Loc B.M.,Ho Chi Minh City University of Pedagogy | Khoa D.T.,Institute for Nuclear Science and Technology | Zegers R.G.T.,Michigan State University
Physical Review C - Nuclear Physics

The charge-exchange (He3,t) scattering to the isobaric analog state (IAS) of the target can be considered as "elastic" scattering of He3 by the isovector term of the optical potential (OP) that flips the projectile isospin. Therefore, the accurately measured charge-exchange scattering cross section for the IAS can be a good probe of the isospin dependence of the OP, which is determined exclusively within the folding model by the difference between the neutron and proton densities and isospin dependence of the nucleon-nucleon interaction. Given the neutron skin of the target related directly to the same density difference, it can be well probed in the analysis of the charge-exchange (He3,t) reactions at medium energies when the two-step processes can be neglected and the t-matrix interaction can be used in the folding calculation. For this purpose, the data of the (He3,t) scattering to the IAS of Zr90 and Pb208 targets at Elab=420 MeV have been analyzed in the distorted wave Born approximation using the double-folded charge-exchange form factor. The neutron skin deduced for these two nuclei turned out to be in a good agreement with the existing database. © 2014 American Physical Society. Source

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