Well-posedness and scalarization in vector optimization

In this paper we study several existing notions of well-posedness for vector optimization problems. We distinguish them into two classes and we establish the hierarchical structure of their relationships. Moreover, we relate vector well-posedness and well-posedness of an appropriate scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are well-posed.well-posedness, vector optimization problems, nonlinear scalarization, generalized convexity.

Well-posed Vector Optimization Problems and Vector Variational Inequalities

In this paper we introduce notions of well-posedness for a vector optimization problem and for a vector variational inequality of differential type, we study their basic properties and we establish the links among them. The proposed concept of well-posedness for a vector optimization problem generalizes the notion of well-setness for scalar optimization problems, introduced in [2]. On the other side, the introduced definition of well-posedness for a vector variational inequality extends the one given in [13] for the scalar case.Keywords: vector optimization, vector variational inequality, well-posedness

On optimality conditions in nonsmooth semi-infinite vector optimization problems (Study on Nonlinear Analysis and Convex Analysis)

In this paper, we establish optimality conditions (both necessary and sufficient) for a nonsmooth semi-infinite vector optimization problem by using the scalarization method

MULTI-OBJECTIVE OPTIMIZATION WITH SOS-CONVEX POLYNOMIALS OVER A POLYNOMIAL MATRIX INEQUALITY (Study on Nonlinear Analysis and Convex Analysis)

This paper is concerned with a multi-objective optimization problem, where the objective functions are sum of square convex polynomials and the constraint is a polynomial matrix inequality. We propose methods for finding (exactly) efficient solutions to the considered multiobjective optimization problem

PARETO OPTIMA OF REINFORCED CONCRETE FRAMES

Optimal design techniques have been extensively appIied to structural design in case of one objectIve iunctIon. They have hardly been used with several objectIve functions. In this paper the multicriterion optimization of reinforced concrete frames is considered and the numerical method for determining the Pareto optimal set of the problem is presented. The criteria to be minimized are the weight of the frame, the volume of reinforcement for the structure and in certain cases the stability criteria. The solution is based on the vector optimization theory