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About 10,000 papers for “functional optimization”

OPTIMIZATION OF FUNCTIONAL PROGRAMS

MARKS, SCOTT CHESSER · Rice Digital Scholarship Archive (Rice University) · 2007

The functional programming style describes computations concisely. The applicative nature of functional programs allows careful analysis of these calculations for optimization. Efficient execution can be achieved by replacing recursive definitions with iterative implementations. The simplified form of functional programs allows effective use of denotational semantics techniques. The same analysis shows a method for implementation as parallel computations using message sending protocols. Networks of distributed processors can be designed in a straightforward way from these results.

Cited by 0

Functional clock schedule optimization

A. Saldanha, Narendra Shenoy, Robert K. Brayton et al. · 2002

All existing algorithms for clock schedule optimization are conservative since they use only topological analysis to estimate the delays of paths between latches. This paper proposes a novel algorithm that accounts for false paths (over several time frames) in level-sensitive sequential circuits to obtain tighter bounds on the optimum clock schedule than previously obtainable.

Cited by 1

Optimization techniques II discrete and functional optimization

Cerf, Max

This book in two volumes provides an overview of continuous, discrete and functional optimization techniques. This second volume is devoted to discrete optimization (problems with integer variables) and functional optimization (problems where the unknown is a function). The topics covered are: • mixed linear programming: cutting methods and tree methods; • combinatorial optimization based on graphs: path, flow, assignment problems . ; • the computation of variations based on Euler-Lagrange conditions and their extensions; • optimal control based on the Pontryaguin maximum principle and its extensions; • numerical methods: differential equations, direct and indirect methods. The emphasis is on understanding the principles rather than on mathematical rigor. Each concept or algorithm is accompanied by a detailed example to help you grasp the main ideas. This book is the result of 30 years of experience and is intended for students, researchers and engineers wishing to acquire a general knowledge in the field of optimization

Cited by 0

Non-Stationary Functional Bilevel Optimization

Jason Bohne, Ieva Petrulionyte, Michael Arbel et al. · arXiv (Cornell University) · 2026

Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios. We propose SmoothFBO, the first algorithm for non-stationary FBO with both theoretical guarantees and practical scalability. SmoothFBO introduces a time-smoothed stochastic hypergradient estimator that reduces variance through a window parameter, enabling stable outer-loop updates with sublinear regret. Importantly, the classical parametric bilevel case is a special reduction of our framework, making SmoothFBO a natural extension to online, non-stationary settings. Empirically, SmoothFBO consistently outperforms existing FBO methods in non-stationary hyperparameter optimization and model-based reinforcement learning, demonstrating its practical effectiveness. Together, these results establish SmoothFBO as a general, theoretically grounded, and practically viable foundation for bilevel optimization in online, non-stationary scenarios.

Cited by 0Open access

Functional Networks Trained by Optimization

Francisco Daniel Filip Duarte · Research Square · 2022

Abstract Artificial neural networks (ANNs) gained much attention due to its capacity to mimic neural cells of living organisms which have intelligence. ANNs and some of its variations, have been applied in text and image recognition, among other applications, and are the basic building blocks of artificial intelligence (AI). A known problem, however, is the impossibility to extract the knowledge achieved by training. To solve this problem, a new neural network is hereby presented, called functional network (FN). This functional network differs from the ANNs basically by the fact that the sigmoid function can be substituted by any mathematical expression, that each functional neuron has multiple inputs and multiple function outputs, and that the trained information can be extracted in the form of a mathematical expression, denominated generative mathematical expression (GME).Although a moderate size FN may give a very large number of possible combinations, requiring very expensive computation efforts on training, recent developments in computation such as quantum computers indicate it increasingly becomes a viable alternative for large patterns and complex models. Thus, the GME of pattern representations can be extracted from a FN in order to simplify AI and numerical modeling tasks in general, such as finite element models (FEM) of structures, or computer fluid dynamic (CFD) models, decreasing overall computation costs.

Cited by 0Open access

Functional Optimization of Carbon Nanotubes

Davis, Taylor, Iverson, Sr. Brian · ScholarsArchive (Brigham Young University) · 2018

The objective of this project was to create, characterize, and optimize carbon nanotube (CNT) films as a surface functionalization strategy through modifying the growth, infiltration, and patterning during fabrication. Carbon nanotubes have drawn attention in various disciplines in the scientific community because of their incredible strength, hardness, wettability (hydrophobicity), as well as their kinetic and electrical properties. At BYU specifically, they are being used in diverse applications including fabrication of superhydrophobic surfaces and interdigitated electrode biosensors. Carbon nanotubes can be delicate with a diameter of only a few nanometers when grown. However, the process of carbon infiltration can be used to layer amorphous carbon on existing nanotubes. As the tubes become thicker, the number of contact points between tubes increases, resulting in a composite, referred to as CICNTs (carbon-infiltrated carbon nanotubes) that is stronger and has a higher thermal and electrical conductivity than carbon nanotubes alone. CNT diameter, contact angle, and sliding angle were examined for varying levels of infiltration to optimize the resulting surfaces for use in condensation heat transfer, creation of anti-microbial surfaces, and other engineering applications.

Cited by 0

Non-Stationary Functional Bilevel Optimization

Jason Bohne, Ieva Petrulionyte, Michael Arbel et al. · ArXiv.org · 2026

Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios. We propose SmoothFBO, the first algorithm for non-stationary FBO with both theoretical guarantees and practical scalability. SmoothFBO introduces a time-smoothed stochastic hypergradient estimator that reduces variance through a window parameter, enabling stable outer-loop updates with sublinear regret. Importantly, the classical parametric bilevel case is a special reduction of our framework, making SmoothFBO a natural extension to online, non-stationary settings. Empirically, SmoothFBO consistently outperforms existing FBO methods in non-stationary hyperparameter optimization and model-based reinforcement learning, demonstrating its practical effectiveness. Together, these results establish SmoothFBO as a general, theoretically grounded, and practically viable foundation for bilevel optimization in online, non-stationary scenarios.

Cited by 0Open access

Neural approximators for functional optimization

R. Zoppoli, Thomas Parisini, Marcello Sanguineti · 2002

Functional optimization problems can be solved analytically only if special assumptions are verified. The approximation method that we propose for the general case is based on the following steps: 1) the decision law is constrained to assume a fixed structure, in which a certain number of free parameters must be optimized, and this enables the functional optimization problem to be reduced to a nonlinear programming one; 2) as a fixed structure, we choose, among various nonlinear approximators, the input/output mapping of multilayer feedforward neural networks; and 3) the resulting nonlinear programming problem is characterized by a highly complex cost function. We propose to minimize it by stochastic programming algorithms. As test-beds for the solving technique, we address a stochastic optimal control problem and an estimation problem, whose solutions are traditionally regarded as difficult tasks.

Cited by 5

Functional optimization properties of median filtering

Guoping Qiu · IEEE Signal Processing Letters · 1994

In this letter, we use a new approach for studying the properties of median filtering. Specifically, using threshold decomposition, it is shown that median filtering operation minimizes a two-term cost function of the output state of the median filter. The first term of the cost function measures the smoothness between the median filter output and its neighbor points within the operation window, and the second term measures the discrepancy between the filter output and its original signal. The results from this study have provided us with a new tool to analyze and understand some of the properties of the median filtering operation, including weighted median filtering.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cited by 30

5G RAN: Functional Split Orchestration Optimization

Salma Matoussi, Ilhem Fajjari, Salvatore Costanzo et al. · IEEE Journal on Selected Areas in Communications · 2020

5G RAN aims to evolve new technologies spanning the Cloud infrastructure, virtualization techniques and Software Defined Network capabilities. Advanced solutions are introduced to split the functions of the Radio Access Network (RAN) between centralized and distributed locations. Such paradigms improve RAN flexibility and reduce the infrastructure deployment cost without impacting the user quality of service. We propose a novel functional split orchestration scheme that aims at minimizing the RAN deployment cost, while considering the requirements of its processing network functions and the capabilities of the Cloud infrastructure. With a fine grained approach on user basis, we show that the proposed solution optimizes both processing and bandwidth resource usage, while minimizing the overall energy consumption compared to i) cell-centric, ii) distributed and iii) centralized Cloud-RAN approaches. Moreover, we evaluate the effectiveness of our proposal in a 5G experimental prototype, based on Open Air Interface (OAI). We show that our solution achieves good performance in terms of total deployment cost and resolution time.

Cited by 56

Functional Analysis, Optimization, and Mathematical Econoinics

1990

Abstract This is a collection of papers dedicated to Leonid Kantorovich and his work. Kantorovich was a Russian mathematician and economist who published in the three areas covered in this book: functional analysis, optimization, and mathematical economics. Kantorovich is credited as being amongst the first inventors of linear programming, the primary technique of optimization. Linear programming consists of creating a matrix of parameters relevant to a system and maximizing the unknown variables using those constraints. Kantorovich then applied this theory to optimal macroeconomic planning in a socialist economy, for which he received the Nobel prize. The present book is dedicated to the memory of Kantorovich, who died in 1986, but is more than a Festschrift. It contains original contributions from several researchers in the USSR never before seen in the US, which enhances the value of the volume. It is organized in a logical sequence from the mathematics to the applications of the theories to concrete problems.

Cited by 7