Process optimization often leads to nonconvex nonlinear programming problems, which may have multiple local optima. There are two major approaches to the identification of the global optimum: deterministic approach an...
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Process optimization often leads to nonconvex nonlinear programming problems, which may have multiple local optima. There are two major approaches to the identification of the global optimum: deterministic approach and stochastic approach. Algorithms based on the deterministic approach guarantee the global optimality of the obtained solution, but are usually applicable to small problems only. Algorithms biased on the stochastic approach, which do not guarantee the global optimality, are applicable to large problems, but inefficient when nonlinear equality constraints are involved. This paper reviews representative deterministic and stochastic global optimization algorithms in order to evaluate their applicability to process design problems, which are generally large, and have many nonlinear equality constraints. Finally, modified stochastic methods are investigated, which use a deterministic local algorithm and a stochastic global algorithm together to be suitable for such problems.
This paper demonstrates a procedure to design an optimal mass to stiffness ratio tensegrity structure. Starting from an initial layout of the structure that defines an allowed set of element connections, the procedure...
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This paper demonstrates a procedure to design an optimal mass to stiffness ratio tensegrity structure. Starting from an initial layout of the structure that defines an allowed set of element connections, the procedure...
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This paper demonstrates a procedure to design an optimal mass to stiffness ratio tensegrity structure. Starting from an initial layout of the structure that defines an allowed set of element connections, the procedure defines positions of the nodal points of the structure, volumes of the elements and their rest lengths yielding a tensegrity structure having smaller compliance for a given load applied then an initial design. To satisfy design requirements strength constraint for all the elements of the structure, buckling constraint for bar elements as well as constraint on geometry of the structure are imposed yielding a nonconvex nonlinear constrained optimization problem. Structural static response is computed using complete nonlinear large displacement model. Examples showing optimal layout of a 2D and 3D structure are shown.
Successive linear programming (SLP) algorithms solve nonlinear optimization problems via a sequence of linear programs. We present an approach for a special class of nonlinear programming problems, which arise in mult...
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Successive linear programming (SLP) algorithms solve nonlinear optimization problems via a sequence of linear programs. We present an approach for a special class of nonlinear programming problems, which arise in multiperiod coal blending. The class of nonlinear programming problems and the solution approach considered in this paper are quite different from previous work. The algorithm is very simple, easy to apply and can be applied to as large a problem as the linear programming code can handle. The quality of solution, produced by the proposed algorithm, is discussed and the results of some test problems, in the real world environment, are provided. (C) 1997 Elsevier Science B.V.
Sufficient conditions for solution Lipschitz continuity, piecewise differentiability, and directional differentiability are presented for parametric nonlinear programs and variational inequalities using the idea of co...
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Sufficient conditions for solution Lipschitz continuity, piecewise differentiability, and directional differentiability are presented for parametric nonlinear programs and variational inequalities using the idea of continuous selections. The gaps between the sufficient conditions obtained here and the weakest possible conditions for the corresponding conclusions are discussed and measured by known regularity conditions.
The solution of nonconvex nonlinear programs with sums of r-convex functions is considered. An algorithm consisting of a sequence of approximating convex programs which converges to a Kuhn-Tucker point is described.
The solution of nonconvex nonlinear programs with sums of r-convex functions is considered. An algorithm consisting of a sequence of approximating convex programs which converges to a Kuhn-Tucker point is described.
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