We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

support vector regression (svr) solves regression problems based on the concept of support vector machine (svm). in this paper, a new model of svr with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadrati...

Topology optimization problem, which involves many design variables, is commonly solved by finite element method, a method must recalculate structure-stiffness matrix each time of analysis. OC method is a good way to solve topology optimization problem, nevertheless, it can not solve multiobjective topology optimization problems. This paper introduces an effective solution to Multi-objective to...

In this paper, several classes of vector F -complementarity problems (in short, VF -CP) and vector F -variational inequalities (in short, VF -VI) with relations determined by nonconvex preferences are introduced in Banach spaces. Some characterizations of solution sets for (VF -CP) and (VF -VI) are also presented. Furthermore, the results obtained are applied to vector optimization problems.

This paper deals with the characterization of solutions for vector equilibrium problems by means of conjugate duality. By using the Fenchel duality we establish variational principles, that is, optimization problems with set-valued objective functions, the solution sets of which contain the ones of the vector equilibrium problems. The set-valued objective mappings depend on the data, but not on...

A comparably new application for support vector machines is their use for meta-modeling the feasible region in constrained optimization problems. Applications have already been developed to optimization problems from the smart grid domain. Still, the problem of a standardized integration of such models into (evolutionary) optimization algorithms was as yet unsolved. We present a new decoder app...

In this note we consider some notions of well-posedness for scalar and vector variational inequalities and we recall their connections with optimization problems. Subsequently, we investigate similar connections between well-posedness of a vector optimization problem and a related variational inequality problem and we present a result obtained with scalar characterizations of vector optimality ...

We consider a vector variational inequality in a finite-dimensional space. A new gap function is proposed, and an equivalent optimization problem for the vector variational inequality is also provided. Under some suitable conditions, we prove that the gap function is directionally differentiable and that any point satisfying the first-order necessary optimality condition for the equivalent opti...

This paper deals with a vector polynomial optimization problem over basic closed semi-algebraic set. By invoking some powerful tools from real geometry, we first introduce the concept called tangency varieties; obtain relationships of Palais–Smale condition, Cerami M-tameness, and properness related to considered problem, in which condition Mangasarian–Fromovitz constraint qualification at infi...