Nonemptiness and Compactness of Solutions Set for Nondifferentiable Multiobjective Optimization Problems

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the nondifferentiable multiobjective optimization problems are proved by using the FKKM theorem and a fixed-point theorem

Hexaaqua­manganese(II) bis­{[N-(3-meth­oxy-2-oxidobenzyl­idene)glycylglycinato]copper(II)} hexa­hydrate

The ligand N-(2-hydr­oxy-3-methoxy­benzyl­idene)glycylglycine (H3 L), a Schiff base derived from glycylglycine and 3-methoxy­salicylaldehyde, was used in the synthesis of a new organic–inorganic coordination complex, [Mn(H2O)6][Cu(C12H11N2O5)]2·6H2O. The MnII atom is located on an inversion center and is coordinated to six water mol­ecules in a slightly distorted octa­hedral geometry. The CuII atom is chelated by the tetra­dentate Schiff base ligand in a distorted CuN2O2 square-planar coordination. In the crystal structure, the complex [Mn(H2O)6]2+ cations and the [CuL]− anions are arranged in columns parallel to the a axis and are held together by O—H⋯O hydrogen bonding. Additional hydrogen bonds of the same type further link the columns into a three-dimensional network