This paper focuses on reducing the dynamic reactions (shaking force, shaking moment, and driving torque) of planar crank-rocker four-bars through counterweight addition. Determining the counterweight mass parameters c...
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This paper focuses on reducing the dynamic reactions (shaking force, shaking moment, and driving torque) of planar crank-rocker four-bars through counterweight addition. Determining the counterweight mass parameters constitutes a nonlinear optimization problem, which suffers from local optima. This paper however proves that it can be reformulated as a convex program, that is, a nonlinear optimization problem of which any local optimum is also globally optimal. Because of this unique property, it is possible to investigate (and by virtue of the guaranteed global optimum, in fact prove) the ultimate limits of counterweight balancing. In a first example a design procedure is presented that is based on graphically representing the ultimate limits in design charts. A second example illustrates the versatility and power of the convex optimization framework by reformulating an earlier counterweight balancing method as a convex program and providing improved numerical results for it.
We consider the problem of minimizing a fractional quadratic problem involving the ratio of two indefinite quadratic functions, subject to a two-sided quadratic form constraint. This formulation is motivated by the so...
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We consider the problem of minimizing a fractional quadratic problem involving the ratio of two indefinite quadratic functions, subject to a two-sided quadratic form constraint. This formulation is motivated by the so-called regularized total least squares (RTLS) problem. A key difficulty with this problem is its nonconvexity, and all current known methods to solve it are guaranteed only to converge to a point satisfying first order necessary optimality conditions. We prove that a global optimal solution to this problem can be found by solving a sequence of very simple convex minimization problems parameterized by a single parameter. As a result, we derive an efficient algorithm that produces an epsilon-global optimal solution in a computational effort of O(n(3) log epsilon(-1)). The algorithm is tested on problems arising from the inverse Laplace transform and image deblurring. Comparison to other well-known RTLS solvers illustrates the attractiveness of our new method.
Approximating a signal or an image with a sparse linear expansion from an overcomplete dictionary of atoms is an extremely useful tool to solve many signal processing problems. Finding the sparsest approximation of a ...
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Approximating a signal or an image with a sparse linear expansion from an overcomplete dictionary of atoms is an extremely useful tool to solve many signal processing problems. Finding the sparsest approximation of a signal from an arbitrary dictionary is a NP-hard problem. Despite this, several algorithms have been proposed that provide suboptimal solutions. However, it is generally difficult to know how close the computed solution is to being "optimal", and whether another algorithm could provide a better result. In this paper we provide a simple test to check whether the output of a sparse approximation algorithm is nearly optimal, in the sense that no significantly different linear expansion from the dictionary can provide both a smaller approximation error and a better sparsity. As a by-product of our theorems, we obtain results on the identifiability of sparse overcomplete models in the presence of noise, for a fairly large class of sparse priors. (C) 2005 Elsevier B.V. All rights reserved.
A multi-objective scheme for structural topology optimization of distributed compliant mechanisms of micro-actuators in MEMS condition is presented in this work, in which mechanical flexibility and structural stiffnes...
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A multi-objective scheme for structural topology optimization of distributed compliant mechanisms of micro-actuators in MEMS condition is presented in this work, in which mechanical flexibility and structural stiffness are both considered as objective functions. The compliant micro-mechanism developed in this way can not only provide sufficient output work but also have sufficient rigidity to resist reaction forces and maintain its shape when holding the work-piece. A density filtering approach is also proposed to eliminate numerical instabilities such as checkerboards, mesh-dependency and one-node connected hinges occurring in resulting mechanisms. SIMP is used as the interpolation scheme to indicate the dependence of material modulus on element-regularized densities. The sequential convex programming method, such as the method of moving asymptotes （MMA）, is used to solve the optimization problem. The validation of the presented methodologies is demonstrated by a typical numerical example.
We consider a chance constrained problem, where one seeks to minimize a convex objective over solutions satisfying, with a given close to one probability, a system of randomly perturbed convex constraints. This proble...
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We consider a chance constrained problem, where one seeks to minimize a convex objective over solutions satisfying, with a given close to one probability, a system of randomly perturbed convex constraints. This problem may happen to be computationally intractable;our goal is to build its computationally tractable approximation, i.e., an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem. We construct a general class of such convex conservative approximations of the corresponding chance constrained problem. Moreover, under the assumptions that the constraints are a. ne in the perturbations and the entries in the perturbation vector are independent-of-each-other random variables, we build a large deviation-type approximation, referred to as "Bernstein approximation," of the chance constrained problem. This approximation is convex and efficiently solvable. We propose a simulation-based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the Bernstein and well-known scenario approximation approaches. Finally, we extend our construction to the case of ambiguous chance constrained problems, where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly, while the chance constraint should be satisfied for every distribution given by this set.
A decomposition scheme for block nonlinear convex programming problems with coupling variables is considered. The possibility is examined of using approximated solutions of subproblems for generating subgradients of t...
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A decomposition scheme for block nonlinear convex programming problems with coupling variables is considered. The possibility is examined of using approximated solutions of subproblems for generating subgradients of the functions that appear in the master problem. A regularization of the original problem that simplifies the master problem is considered.
In this paper, the delayed projection neural network for a class of solving convex programming problem is proposed. The existence of solution and global exponential stability of the proposed network are proved, which ...
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In this paper, the delayed projection neural network for a class of solving convex programming problem is proposed. The existence of solution and global exponential stability of the proposed network are proved, which can guarantee to converge at an exact optimal solution of the convex programming problems. Several examples are given to show the effectiveness of the proposed network.
In this paper, we consider the problem of minimizing a convex separable exponential function over a region defined by a linear equality constraint and bounds on the variables. Such problems are interesting from both t...
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In this paper, we consider the problem of minimizing a convex separable exponential function over a region defined by a linear equality constraint and bounds on the variables. Such problems are interesting from both theoretical and practical point of view because they arise in some mathematical programming problems as well as in various practical problems. Polynomial algorithms are proposed for solving problems of this form and their convergence is proved. Some examples and results of numerical experiments are also presented.
In this paper we study multi issue alternating-offers bargaining in a perfect information finite horizon setting, we determine the pertinent subgame perfect equilibrium, and we provide an algorithm to compute it. The ...
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In this paper we study multi issue alternating-offers bargaining in a perfect information finite horizon setting, we determine the pertinent subgame perfect equilibrium, and we provide an algorithm to compute it. The equilibrium is determined by making a novel use of backward induction together with convex programming techniques in multi issue settings. We show that the agents reach an agreement immediately and that such an agreement is Pareto efficient. Furthermore, we prove that, when the multi issue utility functions are linear, the problem of computing the equilibrium is tractable and the related complexity is polynomial with the number of issues and linear with the deadline of bargaining.
This paper derives a new splitting-based decomposition algorithm for convex stochastic programs. It combines certain attractive features of the progressive hedging algorithm of Rockafellar and Wets, the dynamic splitt...
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This paper derives a new splitting-based decomposition algorithm for convex stochastic programs. It combines certain attractive features of the progressive hedging algorithm of Rockafellar and Wets, the dynamic splitting algorithm of Salinger and Rockafellar and an algorithm of Korf. We give two derivations of our algorithm. The first one is very simple, and the second one yields a preconditioner that resulted in a considerable speed-up in our numerical tests.
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