In this paper we address the problem of optimizing a convex functional subject to linear constraints with uncertainty, which has wide applications in robust control theory. Robust characteristic polynomial assignment ...
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In this paper we address the problem of optimizing a convex functional subject to linear constraints with uncertainty, which has wide applications in robust control theory. Robust characteristic polynomial assignment is first briefly reviewed to motivate the study. The main result of this work is an algorithm which converges to the solution of the uncertain problem. Moreover, special (but important) cases are considered, where finite convergence is guaranteed.
This paper describes a possibility for approximate solution of stochastic programming problems with complete recourse. We replace the static form of linear problem in Lp-space by a sequence of discretized problems in ...
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This paper describes a possibility for approximate solution of stochastic programming problems with complete recourse. We replace the static form of linear problem in Lp-space by a sequence of discretized problems in finite-dimensional spaces. We present conditions that guarantee the convergence of optimal values of discretized problems to the optimal value of the initial problem.
A procedure is described for finding a starting dual feasible solution or terminating by showing that such a solution does not exist, i. e. , by detecting a negative cycle. This dual solution can then be used to conve...
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A procedure is described for finding a starting dual feasible solution or terminating by showing that such a solution does not exist, i. e. , by detecting a negative cycle. This dual solution can then be used to convert the distance matrix into a nonnegative distance matrix where Dijkstra's algorithm can be used.
A linear Fractional Interval programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper an algorithm is developed for solving...
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A linear Fractional Interval programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper an algorithm is developed for solving (FIP) problems. The authors first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations.
A structure-preserving solution approach to large-scale linearprogramming problems that exhibit a nested (multicoupled) angular coefficient structure is presented. The proposed method may be viewed as a recursive ap...
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A structure-preserving solution approach to large-scale linearprogramming problems that exhibit a nested (multicoupled) angular coefficient structure is presented. The proposed method may be viewed as a recursive application of the Gass dualplex method designed for dual angular models, whereby the necessary subproblems are coordinated together by a presented dual pricing relationship. The use of the proposed multicoupled algorithm allows the problem to be solved without any matrix density increases outside the original angular blocks and also allows multiple pivot operations to take place unlike the normal simplex approach. A detailed example is given. Further merit may be found through the proposed method's application to special problem cases of the multicoupled kind.
This paper develops an efficient method for finding the optimal solution to linearmathematical programs on 0–1 variables. It is shown that the lattice (0–1) points satisfying some linear constraint of dimension n c...
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This paper develops an efficient method for finding the optimal solution to linearmathematical programs on 0–1 variables. It is shown that the lattice (0–1) points satisfying some linear constraint of dimension n can equally be represented by those lying in a hypersphere of the same dimension. The lattice points satisfying two linear constraints can be represented by a hypersphere which contains the intersection of the hyperspheres of the two constraints. The method for finding the optimal solution consists of enumerating lattice points which are close to the center of the hypersphere corresponding to the constraints. As soon as a better value of the objective function has been found, than some lower bound, we find a new hypersphere which contains the lattice points of the constraints at which the objective function remains higher than the best known value. We continue in this manner until we have at some stage enumerated all lattice points within a given hypersphere and found none which give a better value.
An efficient Lagrangean dual-based solution method is presented for a linearprogramming problem with a set of separable constraints and one linking constraint. This problem is encountered in solving the generalized ...
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An efficient Lagrangean dual-based solution method is presented for a linearprogramming problem with a set of separable constraints and one linking constraint. This problem is encountered in solving the generalized assignment problem via surrogate duality and constraint aggregation concepts. The search for the optimal Lagrange multiplier is made easy by the convenient characteristics of the Lagrangean subproblems. The method presented here is along the lines of a Lagrangean dual-based method developed in Karwan and Pan (1979) for the linearprogramming relaxation of surrogate subproblems encountered in solving the Fixed Charge Transportation problem. The generator used is one of the versions used by Martello and Toth (1981) and Fisher, et al. (1980) in their work on the generalized assignment problem.
With the development of powerful equation-oriented process simulators, such as SPEEDUP and ASCEND, much research deals with the development of reliable and efficient nonlinear equation solvers for process simulation. ...
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With the development of powerful equation-oriented process simulators, such as SPEEDUP and ASCEND, much research deals with the development of reliable and efficient nonlinear equation solvers for process simulation. However, these methods often approach the treatment of variable bounds or other inequality constraints with ad hoc strategies. Moreover, the absence of a suitable systematic strategy can lead to convergence failures. Instead, we propose an iterative linearprogramming (LP) strategy which automatically deals with inequality constraints and variable bounds. This method reduces to Newton's method in the absence of inequalities and thus has the ability to converge quadratically in the neighborhood of the solution. Moreover, this LP approach can be shown to generate a descent direction for the 1-norm of the constraint violations. Therefore, by applying a line search in the algorithm, one can guarantee progress toward the solution for each nonzero solution to the LP. Other advantages to this approach are that it can deal with many classes of singular points, and the path toward the solution is always contained within the variable bounds. This approach performs very well on a number of small problems and has been implemented within a large-scale modelling system (GAMS). This allows an integration of the method with powerful large-scale LP solvers as well as facilities for quickly generating large process engineering problems. Here we will demonstrate this algorithm for the solution of example problems including pipeline networks and ideal and nonideal distillation problems. It should be mentioned, however, that this algorithm can fail when the LP yields a zero search direction at a nonsolution point. We term this special class of stationary points "pseudosolutions" and derive theoretical properties which characterize them. To recover from pseudosolutions, an "epsilon-strategy" is applied which shifts an active constraint into the feasible region until an impro
We consider LP's of the form max {cx|l≤Ax≤b, L≤x≤U} where,l,b,L,U are nonnegative andA is a 0–1 matrix which looks like “Manhattan Skyline”, i.e. the support of each row is contained in the support of every...
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We consider LP's of the form max {cx|l≤Ax≤b, L≤x≤U} where,l,b,L,U are nonnegative andA is a 0–1 matrix which looks like “Manhattan Skyline”, i.e. the support of each row is contained in the support of every subsequent row. AnO(nm+nlogn) algorithm is presented for solving the problem.
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