In this paper, a large-step analytic center method for smooth convex programming is proposed. The method is a natural implementation of the classical method of centers. It is assumed that the objective and constraint ...
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In this paper, a large-step analytic center method for smooth convex programming is proposed. The method is a natural implementation of the classical method of centers. It is assumed that the objective and constraint functions fulfil the so-called Relative Lipschitz Condition, with Lipschitz constant M > 0. A great advantage of the method, over the existing path-following methods, is that the steps can be made long by performing linesearches. In this method linesearches are performed along the Newton direction with respect to a strictly convex potential function when located far away from the central path. When sufficiently close to this path a lower bound for the optimal value is updated. It is proven that the number of iterations required by the algorithm to converge to an epsilon-optimal solution is O((1 + M-2) root n vertical bar ln epsilon vertical bar) or O((1 + M-2) n vertical bar ln epsilon vertical bar) depending on the updating scheme for the lower bound.
The multiload truss topology design problem is modeled as a minimization of the maximum (with respect to k loading scenarios) compliance subject to equilibium constraints and restrictions on the bar volumes. The probl...
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The multiload truss topology design problem is modeled as a minimization of the maximum (with respect to k loading scenarios) compliance subject to equilibium constraints and restrictions on the bar volumes. The problem may involve a very large number of potential bars so as to allow a rich variety of topologies. The original formulation is in terms of two sets of variables: m bar volumes and n nodal displacements. Several equivalent convex reformulations of this problem are presented. These convex problems, although highly nonlinear, possess nice analytical structure, and therefore can be solved by an interior point potential reduction method associated with appropriate logarithmic barrier for the feasible domain of the problem. For this method, to improve the accuracy of the current approximate solution by an absolute constant factor, it suffices in the worst case to perform O(root km) Newton steps with O(k(3)n(3) + k(2)n(2)m) operations per step.
Let g(y(1), y(2)) be the optimal value of the abstract program which consists in minimizing a convex function f : X --> R boolean OR {+infinity} over a feasible set of the form {x is an element of X : A(1)x = y(1),...
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Let g(y(1), y(2)) be the optimal value of the abstract program which consists in minimizing a convex function f : X --> R boolean OR {+infinity} over a feasible set of the form {x is an element of X : A(1)x = y(1), A(2)x less than or equal to(K) y(2)}. Without assuming the existence of optimal solutions to this minimization problem, we derive formulas for the subdifferential and the approximate subdifferential of g. Several applications are discussed.
A primal-dual version of the proximal point algorithm is developed for linearly constrained convex programming problems. The algorithm is an iterative method to find a saddle point of the Lagrangian of the problem. At...
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We present a primal-dual path following interior algorithm for a class of linearly constrained convex programming problems with non-negative decision variables. We introduce the definition of a Scaled Lipschitz Condit...
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This paper presents a decomposition algorithm for solving convex programming problems with separable structure. The algorithm is obtained through application of the alternating direction method of multipliers to the d...
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The major interest of this paper is to show that, at least in theory, a pair of primal and dual "e{open}-optimal solutions" to a general linear program in Karmarkar's standard form can be obtained by sol...
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A general mixed H 2 /μ optimal control problem is considered. The system consists of a linear-time-Invariant plant with stable weights on the H 2 and μ transfer functions. The controller order can be reduced to as l...
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A general mixed H 2 /μ optimal control problem is considered. The system consists of a linear-time-Invariant plant with stable weights on the H 2 and μ transfer functions. The controller order can be reduced to as low as that of the plant augmented with the H 2 weights. A solution is developed for the optimal fixed order controller which has minimum two-norm for a given value of μ. A numerical approach using sequential quadratic programming is developed to find suboptimal controllers which are as close as desired to optimal. An F-16 longitudinal controller is designed using the mixed technique.
The form-closure and force-closure properties of robotic grasping can be loosely defined as the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, the for...
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The form-closure and force-closure properties of robotic grasping can be loosely defined as the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this paper, the form-closure property of robotic grasping is considered as a purely geometric property of a set of unilateral (contact) constraints, such as those applied on a workpiece by a mechanical fixture. The concept of partial form-closure is introduced and discussed in relation with other concepts appeared in literature, such as accessibility and detachability. An algorithm is proposed to obtain a synthetic geometric description of partial form-closure constraints.
Minimization of the sum of a finite number of concave bottleneck functions subject to linear constraints is studied in the present paper. A related bottleneck linear programming problem which minimizes a single bottle...
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Minimization of the sum of a finite number of concave bottleneck functions subject to linear constraints is studied in the present paper. A related bottleneck linear programming problem which minimizes a single bottleneck objective is constructed whose extreme point solutions provide bounds on the optimal value of the objective function of the problem under consideration. Some k(th) best solution (k greater-than-or-equal-to 1) of this bottleneck linear programming problem satisfying certain conditions is shown to provide an optimal feasible solution of the problem. The proposed algorithm obtains the global optimal solution of the main problem in a finite number of steps. A constrained version of this problem where the optimal feasible solution is required to satisfy an additional constraint is also discussed.
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