This paper gives a systematic study to the general dual-polar Orlicz-Minkowski problem (e.g., Problem 4.1). This problem involves the general dual volume V G (·) recently proposed in [13,15] in order to study the general dual Orlicz-Minkowski problem. As V G (·) extends the volume and the qth dual volume, the general dual-polar Orlicz-Minkowski problem is "polar" to the recently initiated general dual Orlicz-Minkowski problem in [13,15] and "dual" to the newly proposed polar Orlicz-Minkowski problem in [34]. The existence, continuity and uniqueness, if applicable, for the solutions to the general dual-polar Orlicz-Minkowski problem are established. Polytopal solutions and/or counterexamples to the general dual-polar Orlicz-Minkowski problem for discrete measures are also provided. Several variations of the general dual-polar Orlicz-Minkowski problem are discussed as well, in particular the one leading to the general Orlicz-Petty bodies.

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