Asymmetric key algorithms can also be used by two entities to agree on a single key without worrying about eavesdropping by an adversary, which is a tremendously important step in key management. Its security is based on the difficulty of factoring large integers. RSA uses public and private keys that are functions of a pair of large prime numbers. RSA is the best known asymmetric (public key) algorithm, named after its inventors: Rivest, Shamir and Adleman. In principle, you could do the same with RSA too. This is most convenient with encryption schemes such as ElGamal, IES or their elliptic curve variants, where a private key is simply a random number chosen from a given interval. Yes, you can use PBKDF to derive keys for asymmetric encryption too.
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