Showing papers on "Constraint programming published in 1978"

A new approach to differential dynamic programming for discrete time systems

Abstract: This paper proposes a new differential dynamic programming algorithm for solving discrete time optimal control problems with equality and inequality constraints on both control and state variables and proves its convergence. The present algorithm is different from differential dynamic programming algorithms developed in [10]-[15], which can hardly solve optimal control problems with inequality constraints on state variables and whose convergence has not been proved. Composed of iterative methods for solving systems of nonlinear equations, it is based upon Kuhn-Tucker conditions for recurrence relations of dynamic programming. Numerical examples show file efficiency of the present algorithm.

Programming languages and databases

Abstract: Research work in programming languages and in database systems is combating the same problems of scale, change and complexity. This paper looks at the present difficulties of relating persistent data with changing programs. It illustrates the influence that the present interfaces have on programming methodology and algorithm design. It recognises the need for new language primitives to encapsulate database concepts and a few putative primitives are examined. It is suggested that such primitives could simplify the use of databases by programmers. These ideas are illustrated with examples from geometric modelling using Algol 68.

Note—An Efficient Goal Programming Algorithm Using Constraint Partitioning and Variable Elimination

Abstract: An efficient algorithm for solving linear goal programming problems using partitioning and elimination procedures is presented. The algorithm takes advantage of the definition of ordinal preemptive factors in the objective function inherent in most goal programming formulations. Preliminary results indicate that the partitioning algorithm is superior to the existing methods for solving goal programming problems.

Large Scale Nonlinear Programming.

Abstract: : This paper considers first the real world situations which give rise to large nonlinear programming problems. Next the algebraic structure of these problems is analyzed. A brief survey of algorithms for solving them is given with emphasis on those whose computer programs are available. Concluding remarks concern an estimation of future research required in this area. (Author)

A generalized chance constraint programming problem

Abstract: This paper considers a generalized chance constraint programming problem having a controllable probability level Cl. with which the chance constraint should be satisfied. Several properties of this problem are derived and, based on these properties, an algorithm is also proposed.

An Approach to Formal Definitions and Proofs of Programming Principles

Abstract: A method for formal description of programming prinicples is presented in this paper. Programming principles, such as sequential search can be defined and proven even in the absence of an application. We represent a principle as a program scheme which has partially interpreted functions in it. The functions must obey certain input constraints. Use of these ideas in program proving is illustrated with examples.

Technical Note-An Implementation of Surrogate Constraint Duality

Abstract: This paper presents an implementation of surrogate constraint duality in mathematical programming. Motivated by the use of linear programming duality for surrogate constraints in integer linear programs, this implementation is based on geometric programming duality. As a result of this formulation we are able to present an algorithm for surrogate constraint duality and discuss several important properties of the algorithm.

Test problems for constrained nonlinear mathematical programming algorithms

Abstract: The report presents a collection of constrained nonlinear programming problems for use in testing optimization algorithms. The problems vary in size from two variables to one hundred variables with various combinations of linear/nonlinear constraints and objective functions. IBM FORTRAN IV programs were written to provide function values and gradients for the objective function and constraints. Each coded problem was checked at several points against published results, and a validation process was used to check the values of the objective function, constraints, and gradients. The problems were collected from various sources, and many of them have been used by other authors in published results of their algorithm testing. This report should also be useful in an educational setting to provide students with experience in nontrivial problems. Listings of the IBM FORTRAN code are included in this report. 10 tables.

An experimental solution of the general stochastic programming problem

Abstract: After reviewing existing approaches to the general stochastic programming problem, an improved experi mental method is proposed. This method uses a va riety of mathematical programming algorithms and any desired pattern of parameter variation. Statistical analysis of the results allows decision-makers to make probabilistic statements about the values of the decision variables and of the objective function. Illustrative examples are given.

Differential dynamic programming for solving nonlinear programming problems

Abstract: Dynamic programming is one of the methods which utilize special structures of large-scale mathematical programming problems. Conventional dynamic programming, however, can hardly solve mathematical programming problems with many constraints. This paper proposes differential dynamic programming algorithms for solving largescale nonlinear programming problems with many constraints and proves their local convergence. The present algorithms, based upon Kuhn-Tucker conditions for subproblems decomposed by dynamic programming, are composed of iterative methods for solving systems of nonlinear equations. It is shown that the convergence of the present algorithms with Newton's method is R-quadratic. Three numerical examples including the Rosen-Suzuki test problem show the efficiency of the present algorithms.

Optimality and separable linear programming: an additional reminder

Abstract: The assumed global optimum solution obtained in linear programming is not an assumed characteristic of separable linear programming. Separable programming is non-linear programming and must possess certain sufficient conditions for a global optimum to be obtained. The global optimum conditions for separable programming are set forth.

Integer programming and nonlinear integer goal programming applied to system reliability problems

Abstract: The purpose of this thesis is to present the techniques to solve integer constrained nonlinear problems encountered in the system reliability optimization. There have been a number of applications of integer programming techniques to single objective reliability problems, which are first to reformulate the nonlinear integer problems into zero-one linear integer problems and to solve them by zero-one linear integer algorithms. Those techniques are classified into four types. Each integer programming technique is used to solve a numerical example in detail. Few studies have been done on the techniques to solve multiple objective nonlinear integer problems. In this thesis, an algorithm for nonlinear integer goal programming is formulated utilizing a Branch-andbound method and a nonlinear goal programming method. The application of this algorithm is demonstrated by solving reliability problems with single objective and multiple objectives. One interesting feature in using the present algorithm is that the problem is solved by traditional nonlinear search techniques, such as Hooke and Jeeves pattern search, that are originally intended for solving the so called "unconstrained" problem.

The Programming Approach to Development

Abstract: The main task of development strategy is to ensure that resources will be forthcoming to meet the goals of a development programme, and that the resources are allocated efficiently subject to certain constraints. In our earlier discussion of resource allocation we were more concerned with the investment criteria that should be applied in the light of particular goals than with the efficiency with which resources were to be used, or whether the application of the criteria violated certain of the broader constraints mentioned. This was, in fact, a matter of necessity because ordinary marginal analysis is not appropriate to situations in which the aim is to obtain an ‘optimum’ solution subject to constraints which are not precisely specified (or what are called inequalities, e.g. that no more than R resources should be used). Programming, however, can provide a simultaneous solution to the three basic purposes of development planning, which are: the ‘optimum’ allocation of resources; efficiency in the use of resources (through the proper valuation of resources, and the avoidance of ‘social’ waste); and the balance between different branches of the national economy.