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In this paper, we show that a one-layer feedforward neural network with exponential activation functions in the inner layer and logarithmic activation in the output neuron is a universal approximator of convex functions. Such a network represents a family of scaled log-sum exponential functions, here named log-sum-exp (LSET). Under a suitable exponential transformation, the class of LSET functions maps to a family of generalized posynomials GPOST, which we similarly show to be universal approximators for log-log-convex functions. A key feature of an LSET network is that, once it is trained on data, the resulting model is convex in the variables, which makes it readily amenable to efficient design based on convex optimization. Similarly, once a GPOST model is trained on data, it yields a posynomial model that can be efficiently optimized with respect to its variables by using geometric programming (GP). The proposed methodology is illustrated by two numerical examples, in which, first, models are constructed from simulation data of the two physical processes (namely, the level of vibration in a vehicle suspension system, and the peak power generated by the combustion of propane), and then optimization-based design is performed on these models.
This article was published in the following journal.
Name: IEEE transactions on neural networks and learning systems
This paper presents a method to reduce a set of n 2D points to a smaller set of s 2D points with the property that the convex hull on the smaller set is the same as the convex hull of the original big...
This paper presents a neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraints. The proposed neural network endows with a time-varying auxiliary ...
Neural networks are generally built by interleaving (adaptable) linear layers with (fixed) nonlinear activation functions. To increase their flexibility, several authors have proposed methods for adap...
This paper investigates the issue of sampled-data stabilization for Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with time-varying delay. First, the concerned FMNNs are transformed into the ...
We explored the validity of a survey measuring activity spaces for use in health research in a racially/ethnically diverse adult sample (n = 86) living in four Chicago neighborhoods. Participants ...
This study will determine the feasibility of the novel thin convex probe endobronchial ultrasound (TCP-EBUS) in human resected lobes. The primary end point is to clarify the feasibility of...
This study evaluates the performance of a new 1-piece ostomy convex appliance in patients with enterostomy.
The primary objective of this phase II clinical trial is to assess the safety of the Vitala™ device during 12 hours of daily wear with convex products.
Acute circulatory failure is frequent, affecting up to one-third of patients admitted to intensive care units (ICU). Monitoring hemodynamics and cardiac function is therefore a major conce...
The aim of the study is to obtain an understanding of relevant parameters affecting the performance of ostomy products.
BEETLES in the family Curculionidae and the largest family in the order COLEOPTERA. They have a markedly convex shape and many are considered pests.
A computer architecture, implementable in either hardware or software, modeled after biological neural networks. Like the biological system in which the processing capability is a result of the interconnection strengths between arrays of nonlinear processing nodes, computerized neural networks, often called perceptrons or multilayer connectionist models, consist of neuron-like units. A homogeneous group of units makes up a layer. These networks are good at pattern recognition. They are adaptive, performing tasks by example, and thus are better for decision-making than are linear learning machines or cluster analysis. They do not require explicit programming.
Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.
Communications networks connecting various hardware devices together within or between buildings by means of a continuous cable or voice data telephone system.
The statistical manipulation of hierarchically and non-hierarchically nested data. It includes clustered data, such as a sample of subjects within a group of schools. Prevalent in the social, behavioral sciences, and biomedical sciences, both linear and nonlinear regression models are applied.