For a general linear program in Karmarkar's standard form, Fang recently proposed a new approach which would find an epsilon-optimal solution by solving an unconstrained convex dual program. The dual was construct...
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For a general linear program in Karmarkar's standard form, Fang recently proposed a new approach which would find an epsilon-optimal solution by solving an unconstrained convex dual program. The dual was constructed by applying generalized geometric programming theory to a linear programming problem. In this paper we show that Fang's results can be obtained directly using a simple geometric inequality. The new approach provides a better epsilon-optimal solution generation scheme in a simpler way.
Bregman's method is an iterative algorithm for solving optimization problems with convex objective and linear inequality constraints. It generates two sequences: one, the primal one, is known to converge to the so...
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Bregman's method is an iterative algorithm for solving optimization problems with convex objective and linear inequality constraints. It generates two sequences: one, the primal one, is known to converge to the solution of the problem. Under the assumption of smoothness of the objective function at the solution, it is proved that the other sequence, the dual one, converges to a solution of the dual problem, and that the rate of convergence of the primal sequence is at least linear.
A two-phase design used to sample tax records of businesses to obtain annual estimates of Canadian economic production is described. Classification information obtained from units in the first-phase sample is used dur...
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A two-phase design used to sample tax records of businesses to obtain annual estimates of Canadian economic production is described. Classification information obtained from units in the first-phase sample is used during stratification for selection of the second-phase sample. Bernoulli sampling is employed. Given multiple precision constraints, optimal allocation requires solution of a convex programming problem. An approximate method is described and compared to the optimal approach. The efficiency of the two-phase design relative to one-phase alternatives is examined.
A control problem that combines H 2 and H ∞ design objectives for discrete time systems is considered. Under a minimal set of assumptions, we give formulas for solving the problem of minimizing an upper bound for the...
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A control problem that combines H 2 and H ∞ design objectives for discrete time systems is considered. Under a minimal set of assumptions, we give formulas for solving the problem of minimizing an upper bound for the generalized H 2 norm of a closed loop transfer matrix subject to an H ∞ constraint on another closed loop transfer matrix; both, full information and output feedback cases are solved. The formulas are given in terms of a finite dimensional convex program over a constraint set defined by linear matrix inequalities.
In this paper a system identification procedure for MIMO-systems is presented, that yields a model with bounded error. Various model error structures (additive, multiplicative or coprime factor)are considered. The inp...
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In this paper a system identification procedure for MIMO-systems is presented, that yields a model with bounded error. Various model error structures (additive, multiplicative or coprime factor)are considered. The input and out put noise are assumed to be bounded in the frequency domain. An upper bound for the model error is derived, using measured data and the knowledge of the noise. Themodel error bound can be minimized in H ∞ -norm sense by tuning the model parameters. The choice of a linear parametrization will lead to a convex optimization problem, and the algorithms will be robustly convergent.
This paper treats a robustness optimization problem for linear time-invariant systems with real parameteric uncertainty. It is shown that arbitrarily accurate upper and lower bounds on the optimal "robustness mar...
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This paper treats a robustness optimization problem for linear time-invariant systems with real parameteric uncertainty. It is shown that arbitrarily accurate upper and lower bounds on the optimal "robustness margin" can be obtained by finite-dimensional convex optimization. The upper bound is based on a new duality result for a generalized interpolation problem.
In this paper we consider the problem of designing a stabilizing controller which minimizes the H 2 norm of a transfer matrix while maintaining the H ∞ norm of another transfer matrix below a specified level. This pr...
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In this paper we consider the problem of designing a stabilizing controller which minimizes the H 2 norm of a transfer matrix while maintaining the H ∞ norm of another transfer matrix below a specified level. This problem is unsolved, but we approximate the problem by a tractable convex method, and we improve on the H 2 norm bound in the literature. Our main result shows that our formulation is less conservative and the problem can still be solved by convex programming.
Results are presented which generalize the known solution to the problem of minimizing the l 1 norm of the error transfer function. The optimization framework is a dual formulation employing the theory of convex funct...
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Results are presented which generalize the known solution to the problem of minimizing the l 1 norm of the error transfer function. The optimization framework is a dual formulation employing the theory of convex functionals applied to the problem of designing optimal compensators for linear feedback control systems. A wide range of cost functions can be optimized using this theory and it allows a rather general treatment of the topic of time-domain shaping of linear systems. The results obtained can be applied to the mathematically equivalent problems of optimal disturbance rejection and optimal tracking.
This paper addresses the problem of output feedback control design for linear uncertain continuous-time systems, where uncertainties are supposed to belong to convex-bounded domains. Necessary and sufficient condition...
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This paper addresses the problem of output feedback control design for linear uncertain continuous-time systems, where uncertainties are supposed to belong to convex-bounded domains. Necessary and sufficient conditions are provided concerning the existence of a linear static stabilizing output feedback. No extra assumptions such as matching conditions are considered. Based on these conditions, an auxiliary min/max problem can be formulated, allowing us to achieve robust output feedback control using convex programming. These results are illustrated by some examples.
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