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Showing papers on "Discrete optimization published in 1980"



Journal ArticleDOI
TL;DR: In this paper, an improved geometric-series method is presented for converting continuous time models to equivalent discrete time models, and a direct truncation method, a matrix continued fraction method and a geometric series method are presented.

52 citations


Journal ArticleDOI
TL;DR: Some aspects of modelling that influence the performance of optimization methods are discussed, including the construction of smooth models, the transformation of an optimization problem from one category to another, scaling, formulation of constraints, and techniques for special types of models.

16 citations



Journal ArticleDOI
TL;DR: The philosophy of implementing parameter optimization in continuous simulation packages is discussed, and specific examples of the optimizing options of the FORSIM and MACKSIM programs are given.

7 citations




Journal ArticleDOI
TL;DR: In the computer simulation of the process, it was found that the actual overall cost for systems using this on-line multilevel control procedure is within ±10% of the cost resulting from a conventional overall optimal control policy.
Abstract: In this paper an on-line multilevel suboptimal control procedure is developed for large-scale, time-invariant, and discrete linear systems with quadratic performance criterion, and measurement disturbances having arbitrary statistical distributions. The on-line coordination procedure as reported here employs an upper-level intervention through interaction estimates and goal modifications in order to modify lower-level subsystem optimization problems. Their individual controls are applied to the system and the resulting output is estimated by Kalman Type filter and performance information is fedback to the upper level unit. A reference control approach is used to up-date intervention variables over a sequence of time instants to improve on the control being applied to the process. In the computer simulation of the process, it was found that the actual overall cost for systems using this on-line multilevel control procedure is within ±10% of the cost resulting from a conventional overall optimal control policy.

3 citations


Proceedings ArticleDOI
01 Jan 1980
TL;DR: This paper presents and proves the correctness of novel techniques for the mathematical verification of simulation models against sequential machine specifications and shows them to be a formal object whose fidelity to the system can be proved.
Abstract: This paper presents and proves the correctness of novel techniques for the mathematical verification of simulation models against sequential machine specifications. The main idea is to say that a discrete event simulation program simulates a given sequential machine specification if and only if there exists a certain type of mapping from it to the specification. It is first shown that discrete event specifications can be realized by using the traditional formalisms of discrete time systems. Then the two main facilitating results are given. A discrete event simulation of a discrete deterministic system is shown to be a formal object whose fidelity to the system can be proved. A discrete event simulation of a discrete stochastic system is shown to be a formal object whose statistical fidelity to the system can be proved.

3 citations


Journal ArticleDOI
TL;DR: A set of optimal solutions of a particular discrete optimization problem is found by determining a suitable equi-assignment by means of a property based on the Euclidean algorithm for finding the greatest common divisor.

2 citations








Journal ArticleDOI
TL;DR: In this paper, the authors deal with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium, and treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems.
Abstract: This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

01 Feb 1980
TL;DR: It is shown that the well known principle of optimality corresponds to a strong representation of a discrete decision problem by a sequential decision process and that the class of strongly representable discrete decision problems is equivalent to theclass of sequential decision processes which have cost functions satisfying a strict monotonicity condition.
Abstract: : This paper investigates the conditions under which a discrete optimization problem can be formulated as a dynamic program. Following the terminology of (Karp and Held 1967), a discrete optimization problem is formalized as a discrete decision problem and the class of dynamic programs is formalized as a sequential decision process. Necessary and sufficient conditions for the representation in two different senses of a discrete decision problem by a sequential decision process are established. In the first sense (a strong representation) the set of all optimal solutions to the discrete optimization problem is obtainable from the solution of the functional equations of dynamic programming. In the second sense (a weak representation) a nonempty subset of optimal solutions is obtainable from the solution of the functional equations of dynamic programming. It is shown that the well known principle of optimality corresponds to a strong representation. A more general version of the principle of optimality is given which corresponds to a weak representation of a discrete decision problem by a sequential decision process. We also show that the class of strongly representable discrete decision problems is equivalent to the class of sequential decision processes which have cost functions satisfying a strict monotonicity condition. Also a new derivation is given of the result that the class of weakly representable discrete decision problems is equivalent to the class of sequential decision processes which have a cost function satisfying a monotonicity condition. (Author)