You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: A Survey of solution techniques for the partially observed Markov decision process 
Chapter Title:  Smallwood-Sondlk algorithm 
1. Abstract of Cited Paper (BIB001):  This paper treats the discounted cost, optimal control problem for Markov processes with incomplete state information. The optimization approach for these partially observable Markov processes is a generalization of the well-known policy iteration technique for finding optimal stationary policies for completely observable Markov processes. The state space for the problem is the space of state occupancy probability distributions the unit simplex. The development of the algorithm introduces several new ideas, including the class of finitely transient policies, which are shown to possess piecewise linear cost functions. The paper develops easily implemented approximations to stationary policies based on these finitely transient policies and shows that the concave hull of an approximation can be included in the well-known Howard policy improvement algorithm with subsequent convergence. The paper closes with a detailed example illustrating the application of the algorithm to the two-state partially observable Markov process.

Literature Review:
The Smallwood-Sondik (SS) algorithm BIB001 is a successive approximations approach for solving the POMDP and as such is based on determining Hv from v. See BIB002 for a related policy iteration algorithm for the infinite horizon case. The SS algorithm makes extensive use of the fact that H preserves pwl&c. Let F,, be such The fact that the function g is a function of x 6 X can significantly complicate the determination of F'. An approach to determining F' from F (which has been attributed to Monahan) that avoids dealing directly with the issue of determining the function g is as follows. First, determine the set However, G is a large set compared to F (#G = #A(#F ** #Z), where #G is the cardinality of the set G and A ** B = A B) and may contain many unnecessary elements. Second, eliminate as many elements in G as possible to obtain F'. A direct linear programming approach (see BIB001 for further discussion) can be used to reduce the number of elements in G. Consider the following sufficient condition for constructing F' from G" Choose ~ ~ G. If u* = 0, then add ~' to F', where u = maximum u subject to: u <x(~'-~) V~G,