The polynomials that characterize a geometric programming problem are defined by the coefficients c ij and a ijk , which are usually assumed to be constants. In this paper, we allow these parameters to be random varia...
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The polynomials that characterize a geometric programming problem are defined by the coefficients c ij and a ijk , which are usually assumed to be constants. In this paper, we allow these parameters to be random variables with known joint distribution functions and derive the properties of a deterministic equivalent problem corresponding to a multiplicative recourse stochastic model, where the recourse variables rectify in a proportional sense the amount of possible violations of the constraints.
Comparators are the main components in several analog and mixed-signal systems. Design and synthesis of comparator architectures largely remain an analog designer's art. In this work, we present a systematic metho...
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Comparators are the main components in several analog and mixed-signal systems. Design and synthesis of comparator architectures largely remain an analog designer's art. In this work, we present a systematic methodology for designing comparators using the method of constrained optimization. Constrained optimization is an equation-based optimization method and requires accurate equations. We propose a new delay equation for latch-based comparators. The new delay model is based on Adomian decomposition method and gives more accurate delay characteristics compared with the conventional one. The architecture is optimized for total power dissipation with speed, area and noise as the constraints. geometric programming-based automation algorithm and the behavioral model of the comparator architecture are written in MATLAB. The optimized schematic is drawn in Cadence 180 nm technology, and the results are verified with MATLAB.
The strategy presented in this paper differs significantly from existing approaches as we formulate the problem as a standard optimization problem of difference of convex functions. We have developed the necessary and...
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The strategy presented in this paper differs significantly from existing approaches as we formulate the problem as a standard optimization problem of difference of convex functions. We have developed the necessary and sufficient conditions for global solutions in this standard form. The main challenge in the standard form arises from a constraint of the form g(t) = 1, where g is a convex function. We utilize the classical inequality between the weighted arithmetic and harmonic means to overcome this challenge. This enables us to express the optimality conditions as a convex geometric programming problem and employ a predictor-corrector primal-dual interior point method for its solution, with weights updated during the predictor phase. The interior point method solves the dual problem of geometric programming and obtains the primal solution through exponential transformation. We have implemented the algorithm in Fortran 90 and validated it using a set of test problems from the literature. The proposed method successfully solved all the test problems, and the computational results are presented alongside the tested problems and the corresponding solutions found.
In this paper, a neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle to solve geometric progr...
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In this paper, a neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle to solve geometric programming (GP) problems. The main idea is to convert the GP problem into an equivalent convex optimization problem. A neural network model is then constructed for solving the obtained convex programming problem. By employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. The simulation results also show that the proposed neural network is feasible and efficient. (C) 2012 Elsevier B.V. All rights reserved.
geometric programming is extended to include convex quadratic functions. Generalized geometric programming is applied to this class of programs to obtain a convex dual program. Machining economics problems fall into t...
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geometric programming is extended to include convex quadratic functions. Generalized geometric programming is applied to this class of programs to obtain a convex dual program. Machining economics problems fall into this class. Such problems are studied by applying this duality to a nested set of three problems. One problem is zero degree of difficulty and the solution is obtained by solving a simple system of equations. The inclusion of a constraint restricting the force on the tool to be less than or equal to the breaking force provides a more realistic solution. This model is solved as a program with one degree of difficulty. Finally the behavior of the machining cost per part is studied parametrically as a function of axial depth.
We consider the problem of optimally allocating local feedback to the stages of a multistage amplifier. The local feed-back gains affect many performance indexes for the overall amplifier, such as bandwidth, gain, ris...
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We consider the problem of optimally allocating local feedback to the stages of a multistage amplifier. The local feed-back gains affect many performance indexes for the overall amplifier, such as bandwidth, gain, rise time, delay, output signal swing, linearity, and noise performance, in a complicated and nonlinear fashion, making optimization of the feedback gains a challenging problem. In this paper, we show that this problem, though complicated and nonlinear, can be formulated as a special type of optimization problem called geometric programming. geometric programs can be solved globally and efficiently using recently developed interior-point methods. Our method, therefore, gives a complete solution to the problem of optimally allocating local feedback gains, taking into account a wide variety of constraints.
This paper presents the goal geometric programming method in neutrosophic environment. Neutrosophic set is one of the most useful tools to express uncertainty, impreciseness in a more general way compare to fuzzy set ...
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This paper presents the goal geometric programming method in neutrosophic environment. Neutrosophic set is one of the most useful tools to express uncertainty, impreciseness in a more general way compare to fuzzy set and intuitionistic fuzzy set. Thus, the proposed approach is described here as an extension of fuzzy goal geometric programming and intuitionistic fuzzy goal geometric programming. To demonstrate the methodology and applicability of the proposed approach, a multi-objective nonlinear reliability optimization model is taken here and it is evaluated comparing the result obtained by the proposed method with the solution obtained in intuitionistic fuzzy goal geometric programming technique at the end of this paper.
In this paper our main objective is to investigate a deterministic inventory production lot-size model with a permissible delay in payment under a restriction. We analyse our deterministic inventory model under a rest...
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In this paper our main objective is to investigate a deterministic inventory production lot-size model with a permissible delay in payment under a restriction. We analyse our deterministic inventory model under a restriction which will be assumed as the average inventory level. In fact we use in our analysis two approaches: the geometric programming approach;and the Lagrange method. Then a comparison between these two approaches is performed, which is our aim. Finally we deduce some previously published works of other researchers as special cases.
In this paper we provide a simple method to determine the inventory policy of multiple items having varying holding cost using a geometric programming approach. The varying holding cost is considered to be a continuou...
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In this paper we provide a simple method to determine the inventory policy of multiple items having varying holding cost using a geometric programming approach. The varying holding cost is considered to be a continuous function of the order quantity. The EOQ inventory model with constant holding cost and the classical EOQ inventory model without constraints are derived.
We propose an efficient method to compute the maximum likelihood estimator of ordered multinomial probabilities. Using the monotonicity property of the likelihood function, we reformulate the estimation problem as a g...
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We propose an efficient method to compute the maximum likelihood estimator of ordered multinomial probabilities. Using the monotonicity property of the likelihood function, we reformulate the estimation problem as a geometric program, a special type of mathematical optimization problem, which can be transformed into a convex optimization problem, and then solved globally and efficiently. We implement a numerical study to illustrate its computational merits in comparison to the m-PAV algorithm proposed by [Jewell, N.P., Kalbfleisch, J., 2004. Maximum likelihood estimation of ordered multinomial parameters, Biostatistics 5, 291-306]. We also apply our proposed method to the current status data in the above mentioned reference. (C) 2008 Elsevier B.V. All rights reserved.
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