The Greenplum Database originated as an extension of the robust PostgreSQL database and has been re-engineered to support high-volume, high-velocity data in enterprise-grade environments. As an open-source, massively parallel processing (MPP) data warehouse, Greenplum is designed to handle complex analytical queries against big volumes of data.

At its core, Greenplum employs a shared-nothing architecture, distributing data processing tasks across many servers or nodes. This paradigm allows for the horizontal scaling of both data and processing power, which is essential for tackling the demands of big data. Each node operates independently with its own memory, CPU, and disk resources, working in concert to process large datasets more efficiently than traditional single-node databases.

One of the critical aspects of Greenplum is its ability to manage data distribution. The database leverages a table partitioning feature, which divides large tables into smaller, more manageable pieces. It uses a column-oriented storage approach for analytics workloads, which optimizes the I/O performance and accelerates query execution by accessing only the necessary columns of data.

In terms of query optimization, Greenplum incorporates an advanced query planner that transforms SQL queries into execution plans designed to run efficiently across the MPP architecture. This planner is an extension of the PostgreSQL optimizer, tailored to account for the distributed nature of the Greenplum Database.

Data loading and unloading are expedited through parallel mechanisms. The system also supports various data types and allows for the integration of different analytical workloads, including machine learning and artificial intelligence, by facilitating in-database analytics.

The Greenplum Database's capabilities are not limited to analytics. It also offers support for polyglot persistence, allowing users to integrate SQL with procedural languages like Python and R for more sophisticated data manipulation and analytics tasks.

Managing and optimizing a complex, multi-node database like Greenplum can be quite challenging. Despite the administrative challenges it may present, the Greenplum Database is a formidable solution for data warehousing and analytics.