This is an overview of a few possibilities that are open by model theory in applied mathematics. The most attention is paid to the present state and frontiers of the Cauchy method of majorants, approximation of operator equations with finite-dimensional analogs, and the Lagrange multiplier principle in multiobjective decision making. DOI: 10.1134/S1990478909010116 The union of functional analys...

Abstarct: The conventional equilibria problem found in many economics and network models is based on a scalar cost, or a single objective. Recently, equilibria problems based on a vector cost, or multicriteria, have received considerable attention. In this paper, we study a scalarization method for analyzing network equilibria problems with vector-valued cost function. The method is based on th...

Fat conic section and fat conic spline are defined. With well established properties of fat conic splines, the problem of approximating a ruled surface by a tangent smooth cone spline can then be changed as the problem of fitting a plane fat curve by a fat conic spline. Moreover, the fitting error between the ruled surface and the cone spline can be estimated explicitly via fat conic spline fit...

When characterizing optimal solutions of both scalar and vector optimization problems usually constraint qualifications have to be satisfied. By considering sequential characterizations, given for the first time in vector optimization in this paper, this drawback is eliminated. In order to establish them we give first of all sequential characterizations for a convex composed optimization proble...

This paper presents a new method for the numerical solution of nonlinear multiobjective optimization problems with an arbitrary partial ordering in the objective space induced by a closed pointed convex cone. This algorithm is based on the well-known scalarization approach by Pascoletti and Serafini and adaptively controls the scalarization parameters using new sensitivity results. The computed...

Lifting is a procedure for deriving valid inequalities formixed-integer sets from valid inequalities for suitable restrictions of those sets. Lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming and it has been successfully used to solve such problems with branch-and-cut algorithms. Here we generalize the theory of lifting to conic i...

We present a proximal point method to solve multiobjective problems based on the scalarization for maps. We build a family of a convex scalar strict representation of a convex map F with respect to the lexicographic order on R and we add a variant of the logarithmquadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced on the quadratic term and ...

We propose a new threshold signature scheme based on conic curve. The security of the proposed threshold signature scheme is based on the difficulty of computing the DLP in conic curve groups. It can resist some of the known attacks. Since an exciting characteristic of conic is both encoding and decoding over conic are easily implemented, it can be used in the mobile payment system with the lim...