Showing papers on "Continuous optimization published in 1973"

Stochastic optimization problems with nondifferentiable cost functionals

Abstract: In this paper, we examine a class of stochastic optimization problems characterized by nondifferentiability of the objective function. It is shown that, in many cases, the expected value of the objective function is differentiable and, thus, the resulting optimization problem can be solved by using classical analytical or numerical methods. The results are subsequently applied to the solution of a problem of economic resource allocation.

A New Approach to Constrained Function Optimization

Abstract: A new approach to the constrained function optimization problem is presented. It is shown that the ordinary Lagrange multiplier method and the penalty function method may be generalized and combined, and the new concept ofmultiplier function is introduced. The problem may then be converted into an unconstrained well-conditioned optimization problem. Methods for numerical solution are discussed, and new algorithms are derived.

A combined decomposition and coordination method in large dimension optimization problems

Abstract: In this article, the authors present a method for the decomposition of complex problems which uses as coordination magnitudes the variables of interconnection between subsystems and the associated Lagrangian parameters. This method thus uses a combined coordination by simultaneous action on the criterion function and on the model of each subsystem. The principles of the method are discussed along with static and dynamic optimization problems while defining the local lower-level optimization subproblems, proposing coordinating algorithms for the higher level, and presenting the con vergence studies relative to these algorithms.

Response Surface Optimization when Experimental Factors are Subject to Costs and Constraints

Abstract: This paper deals with problems of response surface optimization in which the control variables and responses are subject to costs and constraints. Relationships between control variables and the cost or constraint functions are treated as additional response surfaces if explicit algebraic models are unavailable. Optimization methods are suggested which are based on gradient search and nonlinear programming techniques. To assure operating conditions within the specified constraint set a method based on feasible directions is used to control the search pattern. A scale-invariant gradient search method is suggested. Because it leads to an economical path to the maximum point the method has been dubbed “cheapest ascent.” The selection of measurement scales for the control variables is also discussed.

The solution of discrete linear optimization problems by neighborhood-search techniques

Abstract: A process and apparatus for forming a wide variety of air-laid nonwoven webs, with the apparatus including plural pairs of spaced parallel oppositely rotating lickerins, each pair having a movable divider plate therebetween. The lickerins individualize fibers from separate fibrous sources, which may be similar or dissimilar, and high speed air streams are caused to flow past each individual lickerin, through a mixing zone between each pair of lickerins to form combined streams, and into a common mixing zone above a fiber collecting means to form a composite stream. The individualized fibers are doffed from the lickerins by the high speed air streams and are entrained therein, and divider plates between each pair of lickerins are adjustable through a range of positions for controlling the degree of intermixing of the entrained fibers in the combined streams. A further divider plate is mounted in adjustable relationship with respect to the common mixing zone to control the degree to which the combined streams and entrained fibers intermix in forming the composite stream. The air streams may be generated by a single suction source below the fiber collecting means, or by separate individually controlled suction sources on opposite sides of the further divider plates, which may be individually adjusted to further vary the web that is formed on the fiber collecting means. The further divider plate is preferably removably mounted so that a further material, such as a reinforcing material or an adhesive can be introduced into the composite stream and resulting web, if desired.

Nonlinear constrained optimization of filled polyesters

Abstract: An efficient method for optimization of a formulation problem subject to nonlinear constraints was demonstrated. Specifically, a nine-variable polyester-filler system was investigated experimentally. The investigation included selection of an efficient experimental design, regression analysis, and study of optimization methods. Recommended procedures are reported, along with examples and discussion of several typical applications.