No abstract

No abstract

In this paper we consider the solvability of a non-convex regular polynomial vector optimization problem on a nonempty closed set. We introduce regularity conditions for the polynomial vector optimization problem and study properties and characterizations of the regularity conditions. Under the regularity conditions, we study nonemptiness and boundedness of the solution sets of the problem. As a consequence, we establish two Frank-Wolfe type theorems for the non-convex polynomial vector optimization problem.Finally, we investigate the solution stability of the non-convex regular polynomial vector optimization problem.

Detecting impact craters on the Martian surface is a critical component of studying Martian geomorphology and planetary evolution. Accurately determining impact crater boundaries, which are distinguishable geomorphic units, is important work in geological and geomorphological mapping. The Martian topography is more complex than that of the Moon, making the accurate detection of impact crater boundaries challenging. Currently, most techniques concentrate on replacing impact craters with circles or points. Accurate boundaries are more challenging to identify than simple circles. Therefore, a boundary delineator for Martian crater instances (BDMCI) using fusion data is proposed. First, the optical image, digital elevation model (DEM), and slope of elevation difference after filling the DEM (called slope of EL_Diff to highlight the boundaries of craters) were used in combination. Second, a benchmark dataset with annotations for accurate impact crater boundaries was created, and sample regions were chosen using prior geospatial knowledge and an optimization strategy for the proposed BDMCI framework. Third, the multiple models were fused to train at various scales using deep learning. To repair patch junction fractures, several postprocessing methods were devised. The proposed BDMCI framework was also used to expand the catalog of Martian impact craters between 65°S and 65°N. This study provides a reference for identifying terrain features and demonstrates the potential of deep learning algorithms in planetary science research.

No abstract