Automated parameter search has become a standard method in the modeling of neural systems. These studies could potentially take advantage of recent developments in nonlinearoptimization, and the availability of softw...
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ISBN:
(数字)9781728169262
ISBN:
(纸本)9781728169262
Automated parameter search has become a standard method in the modeling of neural systems. These studies could potentially take advantage of recent developments in nonlinearoptimization, and the availability of software packages containing high-quality implementations of algorithms that proved useful in other domains. However, a systematic comparison of the available algorithms for problems that are typical in neuroscience has not been performed. We developed a software tool for fitting the parameters of neural models, which provides intuitive, uniform access to a variety of state-of-the-art optimizationalgorithms implemented by four different Python packages. We also established a set of benchmark problems of different complexity that involve a variety of widely used neuronal models. We then used our optimization tool to systematically evaluate the performance of the algorithms on our set of benchmark problems. We found that several evolutionary and related algorithms consistently provided good solutions for all of our benchmarks. However, the relative performance of the different methods, both in terms of the quality of the final result and in terms of convergence speed, depended substantially on the nature of the problem. We hope that our software tool and benchmarking results will facilitate the choice and application of the best parameter-fitting methods in neuroscientific research.
This article details an investigation into the computational performance of algorithms used for solving a convex formulation of the optimization problem associated with model predictive control for energy management i...
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This article details an investigation into the computational performance of algorithms used for solving a convex formulation of the optimization problem associated with model predictive control for energy management in hybrid electric vehicles with nonlinear losses. A projected interior-point method is proposed, where the size and complexity of the Newton step matrix inversion is reduced by applying inequality constraints on the control input as a projection, and its properties are demonstrated through simulation in comparison with an alternating direction method of multipliers (ADMM) algorithm and a general purpose convex optimizationsoftware CVX. It is found that the ADMM algorithm has favorable properties when a solution with modest accuracy is required, whereas the projected interior-point method is favorable when high accuracy is required, and that both are significantly faster than CVX.
In this paper, the task to start the operation of an evaporation system with hybrid dynamics is considered. The evaporator system was provided as a benchmark for hybrid control by a major chemical company. Rigorous mo...
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In this paper, the task to start the operation of an evaporation system with hybrid dynamics is considered. The evaporator system was provided as a benchmark for hybrid control by a major chemical company. Rigorous modeling gives rise to a hybrid automaton with high-dimensional nonlinear DAE dynamics that describe the continuous evolution in different discrete modes of operation. The problem of optimized start-up is solved by a branch-and-bound algorithm with embedded nonlinear dynamic optimization over a finite look-ahead horizon. The nonlinearoptimization problems are solved by nonlinear programming and by evolutionary algorithms. Important elements of this formulation of the optimization problems are the introduction of a dynamic choice of the time intervals over which the zero-order hold controls are constant and the utilization of tailored penalty functions in order to obtain solutions which are close to the bounds of the feasible state regions. The two approaches are compared with respect to their performance for the evaporation system. 2007 Elsevier Ltd. All rights reserved.
We present a computationally efficient implementation of an interior point algorithm for solving large-scale problems arising in stochastic linear programming and robust optimization. A matrix factorization procedure ...
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We present a computationally efficient implementation of an interior point algorithm for solving large-scale problems arising in stochastic linear programming and robust optimization. A matrix factorization procedure is employed that exploits the structure of the constraint matrix, and it is implemented on parallel computers. The implementation is perfectly scalable. Extensive computational results are reported for a library of standard test problems from stochastic linear programming, and also for robust optimization formulations. The results show that the codes are efficient and stable for problems with thousands of scenarios. Test problems with 130 thousand scenarios, and a deterministic equivalent linear programming formulation with 2.6 million constraints and 18.2 million variables, are solved successfully.
This paper considers the number of inner iterations required per outer iteration for the algorithm proposed by Conn er al. [9]. We show that asymptotically, under suitable reasonable assumptions, a single inner iterat...
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This paper considers the number of inner iterations required per outer iteration for the algorithm proposed by Conn er al. [9]. We show that asymptotically, under suitable reasonable assumptions, a single inner iteration suffices.
In this paper we deal with the iterative computation of negative curvature directions of an objective function, within large scale optimization frameworks. In particular, suitable directions of negative curvature of t...
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In this paper we deal with the iterative computation of negative curvature directions of an objective function, within large scale optimization frameworks. In particular, suitable directions of negative curvature of the objective function represent an essential tool, to guarantee convergence to second order critical points. However, an '' adequate '' negative curvature direction is often required to have a good resemblance to an eigenvector corresponding to the smallest eigenvalue of the Hessian matrix. Thus, its computation may be a very difficult task on large scale problems. Several strategies proposed in literature compute such a direction relying on matrix factorizations, so that they may be inefficient or even impracticable in a large scale setting. On the other hand, the iterative methods proposed either need to store a large matrix, or they need to rerun the recurrence. On this guideline, in this paper we propose the use of an iterative method, based on a planar Conjugate Gradient scheme. Under mild assumptions, we provide theory for using the latter method to compute adequate negative curvature directions, within optimization frameworks. In our proposal any matrix storage is avoided, along with any additional rerun.
ELSO is an environment for the solution of large-scale optimization problems. With ELSO the user is required to provide only code for the evaluation of a partially separable function. ELSO exploits the partial separab...
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ELSO is an environment for the solution of large-scale optimization problems. With ELSO the user is required to provide only code for the evaluation of a partially separable function. ELSO exploits the partial separability structure of the function to compute the gradient efficiently using automatic differentiation. We demonstrate ELSO's efficiency by comparing the various options available in ELSO. Our conclusion is that the hybrid option in ELSO provides performance comparable to the hand-coded option, while having the significant advantage of not requiring a hand-coded gradient or the sparsity pattern of the partially separable function. In our test problems, which have carefully coded gradients, the computing time for the hybrid AD option is within a factor of two of the hand-coded option.
The satisfiability problem modulo the nonlinear real arithmetic (NRA) theory serves as the foundation for a wide range of important applications, such as model checking, program analysis, and software testing. However...
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ISBN:
(纸本)9798350329964
The satisfiability problem modulo the nonlinear real arithmetic (NRA) theory serves as the foundation for a wide range of important applications, such as model checking, program analysis, and software testing. However, due to the high computational complexity, developing efficient solving algorithms for this problem has consistently presented a substantial challenge. We present a hybrid SMT(NRA) solver, called NRAgo, which combines the efficiency of gradient-based optimization method with the completeness of algebraic solving algorithm. With our approach, the practical performance on many satisfiable instances is substantially improved. The experimental evaluation shows that NRAgo achieves remarkable acceleration effects on a set of challenging SMT(NRA) benchmarks that are hard to solve for state-of-the-art SMT solvers.
This paper is concerned with the numerical solution of a Karush-Kuhn-Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior-Point (IP) approach. In this fra...
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This paper is concerned with the numerical solution of a Karush-Kuhn-Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior-Point (IP) approach. In this framework, we discuss the effectiveness of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the implementation details of these algorithms in an IP scheme and we report the results of a numerical comparison on a set of large scale test-problems arising from the discretization of elliptic control problems.
System identification is an important means for obtaining dynamical models for process control applications;experimental testing represents the most time-consuming step in this task. The design of constrained, '...
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System identification is an important means for obtaining dynamical models for process control applications;experimental testing represents the most time-consuming step in this task. The design of constrained, '' plant-friendly '' multisine input signals that optimize a geometric discrepancy criterion arising from Weyl's Theorem is examined in this paper. Such signals are meaningful for data-centric estimation methods, where uniform coverage of the output state-space is critical. The usefulness of this problem formulation is demonstrated by applying it to a linear problem example and to the nonlinear, highly interactive distillation column model developed by Weischedel and McAvoy. The optimization problem includes a search for both the Fourier coefficients and phases in the multisine signal, resulting in an uniformly distributed output signal displaying a desirable balance between high and low gain directions. The solution involves very little user intervention (which enhances its practical usefulness) and has great benefits compared to multisine signals that minimize crest factor. The constrained nonlinearoptimization problems that are solved represent challenges even for high-performanceoptimizationsoftware.
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