A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set.
A rectifier is a electrical device that converts alternating current to direct current, a process known as rectification. Rectifiers are used as components of power supplies and as detectors of radio signals. Rectifiers may be made of solid state diodes, vacuum tube diodes, mercury arc valves, and other technologies.
A rectifier usually means a (set of) electronic components that turns AC into DC, which you need to charge a battery for instance. A regulator-well, it regulates something. Considering the category the question is posted in I'd say it regulates the charging of the battery and/or the output voltage of the rectifier.