This paper proposes a method to determine trajectories of dynamic systems that steer between two end points while satisfying linear inequality constraints arising from limits on states and inputs. The method exploits ...
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This paper proposes a method to determine trajectories of dynamic systems that steer between two end points while satisfying linear inequality constraints arising from limits on states and inputs. The method exploits the structure of the dynamic system to eliminate the state equations. The linear inequalities on inputs and states are replaced by a finite set of linear inequalities on the mode coefficients and changing the problem of trajectory generation to finding a convex polytope on the mode coefficients. The procedure is demonstrated in an example and verified experimentally.
In the present paper the logarithmic barrier method applied to the linearly constrained convex optimization problems is studied from the view point of classical path-following algorithms. In particular, the radius of ...
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This paper investigates and unifies several relative nonlinear optimization problems in locally convex topological vector spaces or in convex spaces. The main generalization including some unified forms is the weaking...
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A detailed description of a path-following Interior point algorithm for constrained convex programs is presented. The algorithm employs a truncated logarithmic barrier function, which is particularly suitable to probl...
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A detailed description of a path-following Interior point algorithm for constrained convex programs is presented. The algorithm employs a truncated logarithmic barrier function, which is particularly suitable to problems with many nonactive constraints. A special version of the algorithm is adopted to minmax problems. Extensive testing of the algorithms on large-scale Structural Optimization problems (truss topology design, shape design with optimized material) demonstrate their efficiency.
In a generalised H 2 optimal control problem, the conventional H 2 norm is replaced by an operator norm, A stabilising controller is sought such that the closed loop gain from time domain input disturbances in L 2 to ...
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In a generalised H 2 optimal control problem, the conventional H 2 norm is replaced by an operator norm, A stabilising controller is sought such that the closed loop gain from time domain input disturbances in L 2 to time domain regulated outputs in L ∞ is minimised, A solution to this problem can be obtained by using a finite dimensional convex programme for weight selection in an LQR problem. Both continuous- and discrete-time versions of problem are considered, and, following the technique of Rotea (1993) the problem is reduced to one of finding a state feedback controller for an auxiliary system. In general, the weight selection method offers a potentially reduced computational burden compared with that in Rotea (1993).
We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that oc...
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We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B-functions (generalized Bregman functions).
Synchronous vibration is the most common form of vibration in rotorbearing systems. Open-loop controllers, in conjunction with magnetic bearings, have been shown to be very effective in controlling synchronous vibrati...
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Synchronous vibration is the most common form of vibration in rotorbearing systems. Open-loop controllers, in conjunction with magnetic bearings, have been shown to be very effective in controlling synchronous vibration in flexible rotor-bearing systems. A well-known open-loop controller, called a mini-least-squares controller, minimises the measured rotor vibration in a least-squares sense. In this paper, it is shown how convex programming can be used to design mini-major-axis controllers, which minimise the largest measured rotor displacement. A numerical example illustrates the potential improvement in performance of mini-major-axis controllers compared to mini-least-squares controllers.
The minimum covering hypersphere problem is defined as to find a hypersphere of minimum radius enclosing a finite set of given points in IRn. A hypersphere is a set S(c,r) = {x is an element of IRn : d(x,c) less than ...
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The minimum covering hypersphere problem is defined as to find a hypersphere of minimum radius enclosing a finite set of given points in IRn. A hypersphere is a set S(c,r) = {x is an element of IRn : d(x,c) less than or equal to r}, where c is the center of S, r is the radius of S and d(x,c) is the Euclidean distance between x and c, i.e., d(x,c) = l(2)(x - c). We consider the extension of this problem when d(x,c) is given by any l(pb)-norm, where 1 < p < infinity and b = (b(1),..., b(n)) with b(j) > 0, j = 1,..., n, then S(c,r) is called an l(pb)-hypersphere. in particular for p = 2 and b(j) = 1, j = 1,..., n, we obtain the l(2)-norm. We study some properties and propose some primal and dual algorithms for the extended problem, which are based on the feasible directions method and on the Wolfe duality theory. By computational experiments, we compare the proposed algorithms and show that they can be used to approximate the smallest l(pb)-hypersphere enclosing a large set of points in IRn.
Based on the concept in Part 1, Theory and General Case, algorithms to determine the constrained R-T characteristic curve are established for convex constrained machining economics problems. The first algorithm is for...
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Based on the concept in Part 1, Theory and General Case, algorithms to determine the constrained R-T characteristic curve are established for convex constrained machining economics problems. The first algorithm is for posynomial problems with the linear-logarithmic tool life equation. The R-T curve may be determined by applying the simplex method to the log-dual problems. Sensitivity analysis of the optimal simplex tableau enables obtaining the loci of optima easily. The second algorithm is for the quadratic poslygnomial problems with quadratic-logarithmic tool life equation using the property of primal-dual feasibility. End milling examples constructed in Part 1 illustrate the algorithm comparing to the exhaustive method.
The subgradient method is generalized to the context of Riemannian manifolds. The motivation can be seen in non-Euclidean metrics that occur in interior-point methods. In that frame, the natural curves for local steps...
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The subgradient method is generalized to the context of Riemannian manifolds. The motivation can be seen in non-Euclidean metrics that occur in interior-point methods. In that frame, the natural curves for local steps are the geodesics relative to the specific Riemannian manifold. In this paper, the influence of the sectional curvature of the manifold on the convergence of the method is discussed, as well as the proof of convergence if the sectional curvature is nonnegative.
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