We provide fundamental results of the structural theory computably separable models and consider applications this to effective linear orders theoretical informatics.

In this paper we propose a unifying approach to the study of recursive economic problems. Postulating an aggregator function as the fundamental expression of tastes, we explore conditions under which a utility function can be constructed. We also modify the usual dynamic programming arguments to include this class of models. We show that Bellman’s equation still holds, so many results known for...

This correspondence describes an approach to reducing the computational cost of document image decoding by viewing it as a heuristic search problem. The kernel of the approach is a modi ed dynamic programming (DP) algorithm, called the iterated complete path (ICP) algorithm, that is intended for use with separable source models. A set of heuristic functions are presented for decoding formatted ...

This paper presents a Branch and Bound method for a nonconvex integer quadratic programming problem with a separable objective function over a bounded box. For this problem, a special branch method is constructed, which has a property that if a box has been partitioned into 2 sub-boxes, then at least one sub-box can be deleted. We analyze the complexity of the algorithm, and prove that it is be...

We describe a primal-dual interior point algorithm for a class of convex separable programming problems subject to linear constraints. Each iteration updates a penalty parameter and finds a Newton step associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem for that parameter. It is shown that the duality gap is reduc...

We explore the idea of obtaining bounds on the value of an optimization problem from a discrete relaxation based on binary decision diagrams (BDDs). We show how to construct a BDD that represents a relaxation of a 0–1 optimization problem, and how to obtain a bound for a separable objective function by solving a shortest (or longest) path problem in the BDD. As a test case we apply the method t...

We consider a single-period portfolio selection problem which consists of minimizing the total transaction cost subject to different types of constraints on feasible portfolios. The transaction cost function is separable, i.e., it is the sum of the transaction cost associated with each trade, but discontinuous. This optimization problem is nonconvex and very hard to solve. We investigate in thi...