Globular clusters in the Milky Way have characteristic velocity dispersions that are consistent with the predictions of Newtonian gravity, and may be at odds with Modified Newtonian Dynamics (MOND) and possibly the cold dark matter model. We discuss a modified gravity (MOG) theory that can successfully model the velocity dispersions of GCs in the Galactic neighborhood. MOG produces velocity dis...

⎯In this paper, we construct a pair of Mond-Weir type second order symmetric dual problems, in which the objective function contains support function and is, therefore, nondifferentiable. For this pair of problems, we validate weak, strong and converse duality theorems under pseudobonvexity – pseudoboncavity assumption on the kernel function that appears in the problems. A second order self dua...

Fritz John and Kuhn-Tucker type necessary optimality conditions for a Pareto optimal (efficient) solution of a multiobjective control problem are obtained by first reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir ...

Globular clusters in the Milky Way have characteristic velocity dispersions that are consistent with the predictions of Newtonian gravity, and may be at odds with Modified Newtonian Dynamics (MOND) and possibly the cold dark matter model. We discuss a modified gravity (MOG) theory that can successfully model the velocity dispersions of GCs in the Galactic neighborhood. MOG produces velocity dis...

Milgrom’s Modified Newtonian dynamics (MOND) provides an efficient way to summarize phenomenology of galaxies which does not lean on the notion of dark matter; it has great predictive power. Here I briefly review MOND as well as its implementation as a nonrelativistic modified gravity theory, AQUAL. Gravitational lensing and cosmology call for a relativistic gravity theory different from genera...

In this paper, Antczak’s -approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the -saddle points of the associated -approximated vector optimisation problems. We introduce an -Lagrange function for a constructed -approximated vector optimisation problem and present some modified -saddle point results. Furthermore, we construct an -ap...

Any viable theory of modified Newtonian dynamics (MOND) as modified gravity is likely to require fields in addition to the usual tensor field of General Relativity. For such theories the MOND phenomenology emerges as an effective fifth force probably associated with a scalar field. Here I consider the constraints imposed upon such theories by solar system phenomenology, primarily by the absence...

Globular clusters (GCs) in the Milky Way have characteristic velocity dispersions that are consistent with the predictions of Newtonian gravity, and may be at odds with Modified Newtonian Dynamics (MOND) and possibly the cold dark matter model. We discuss a modified gravity (MOG) theory that can successfully model the velocity dispersions of GCs in the Galactic neighborhood. MOG produces veloci...