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In this paper we study the stability of the minimal solutions of set optimization problems. We provide sufficient conditions for the upper and lower semicontinuity and compactness of the minimal solutions of parametric set optimization problems whose objective values are not necessarily compact. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study Levitin–Polyak (LPin short) well-posedness for set optimization problems. We define the global notions of metrically well-setness and metricallyLPwell-setness and the pointwise notions ofLPwell-posedness, strongly DH-well-posedness and strongly B-well-posedness for set optimization problems. Using a scalarization function defined by means of the point-to-set distance, we characterize theLPwell-posedness and the metrically well-setness of a set optimization problem through theLPwell-posedness and the metrically well-setness of a scalar optimization problem, respectively. [ABSTRACT FROM AUTHOR]

In this paper we characterize the cone-continuous set-valued maps in terms of the semicontinuity of certain extended real-valued functions, defined by means of the polar cone, some new Gerstewitz-like scalarization functions, or by some new nonlinear scalarization functions based on the point-to-set distance. [ABSTRACT FROM PUBLISHER]