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Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices

Faouzi Ben Charrada, Sana Ezouaoui, Zaher Mahjoub (2011)

RAIRO - Operations Research - Recherche Opérationnelle

This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...

Greedy algorithms for optimal computing of matrix chain products involving square dense and triangular matrices

Faouzi Ben Charrada, Sana Ezouaoui, Zaher Mahjoub (2011)

RAIRO - Operations Research

This paper addresses a combinatorial optimization problem (COP), namely a variant of the (standard) matrix chain product (MCP) problem where the matrices are square and either dense (i.e. full) or lower/upper triangular. Given a matrix chain of length n, we first present a dynamic programming algorithm (DPA) adapted from the well known standard algorithm and having the same O(n3) complexity. We then design and analyse two optimal O(n) greedy algorithms leading in general to different optimal solutions...

Growth rates and average optimality in risk-sensitive Markov decision chains

Karel Sladký (2008)

Kybernetika

In this note we focus attention on characterizations of policies maximizing growth rate of expected utility, along with average of the associated certainty equivalent, in risk-sensitive Markov decision chains with finite state and action spaces. In contrast to the existing literature the problem is handled by methods of stochastic dynamic programming on condition that the transition probabilities are replaced by general nonnegative matrices. Using the block-triangular decomposition of a collection...

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