scholarly journals Affine-invariant contracting-point methods for Convex Optimization

2022 ◽  
Author(s):  
Nikita Doikov ◽  
Yurii Nesterov
Keyword(s):  
Complexity Analysis ◽  
Trust Region ◽  
Optimization Methods ◽  
Computational Time ◽  
Smoothness Condition ◽  
Affine Invariant ◽  
Complexity Bounds ◽  
Global Rate ◽  
Smooth Part ◽  
New Interpretation

AbstractIn this paper, we develop new affine-invariant algorithms for solving composite convex minimization problems with bounded domain. We present a general framework of Contracting-Point methods, which solve at each iteration an auxiliary subproblem restricting the smooth part of the objective function onto contraction of the initial domain. This framework provides us with a systematic way for developing optimization methods of different order, endowed with the global complexity bounds. We show that using an appropriate affine-invariant smoothness condition, it is possible to implement one iteration of the Contracting-Point method by one step of the pure tensor method of degree $$p \ge 1$$ p ≥ 1 . The resulting global rate of convergence in functional residual is then $${\mathcal {O}}(1 / k^p)$$ O ( 1 / k p ) , where k is the iteration counter. It is important that all constants in our bounds are affine-invariant. For $$p = 1$$ p = 1 , our scheme recovers well-known Frank–Wolfe algorithm, providing it with a new interpretation by a general perspective of tensor methods. Finally, within our framework, we present efficient implementation and total complexity analysis of the inexact second-order scheme $$(p = 2)$$ ( p = 2 ) , called Contracting Newton method. It can be seen as a proper implementation of the trust-region idea. Preliminary numerical results confirm its good practical performance both in the number of iterations, and in computational time.

scholarly journals Application and benchmarking of a direct method to optimize the fuel consumption of a diesel electric locomotive

2018 ◽  
Vol 232 (9) ◽  
pp. 2272-2289 ◽  
Author(s):  
V Macian ◽  
C Guardiola ◽  
B Pla ◽  
A Reig
Keyword(s):  
Optimal Control ◽  
Direct Method ◽  
Minimum Principle ◽  
Optimization Technique ◽  
Direct Methods ◽  
Optimization Methods ◽  
Computational Time ◽  
Electric Locomotive ◽  
Pontryagin Minimum Principle ◽  
A Direct Method

This paper addresses the optimal control of a long-haul passenger train to deliver minimum-fuel operations. Contrary to the common Pontryagin minimum principle approach in railroad-related literature, this work addresses this optimal control problem with a direct method of optimization, the use of which is still marginal in this field. The implementation of a particular direct method based on the Euler collocation scheme and its transcription into a nonlinear problem are described in detail. In this paper, this optimization technique is benchmarked with well-known optimization methods in the literature, namely dynamic programming and the Pontryagin minimum principle, by simulating a real route. The results showed that the direct methods are on the same level of optimality compared with other algorithms while requiring reduced computational time and memory and being able to handle very complex dynamic systems. The performance of the direct method is also compared to the real trajectory followed by the train operator and exhibits up to 20% of fuel saving in the example route.

scholarly journals Comparison of Local and Global Optimization Methods for Calibration of a 3D Morphodynamic Model of a Curved Channel

Water ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 1333
Author(s):  
Vahid Shoarinezhad ◽  
Silke Wieprecht ◽  
Stefan Haun
Keyword(s):  
Global Optimization ◽  
Sediment Transport ◽  
Numerical Model ◽  
Numerical Models ◽  
Optimization Algorithms ◽  
Flow Characteristics ◽  
Optimization Methods ◽  
Computational Time ◽  
Curved Channel ◽  
Time Model

In curved channels, the flow characteristics, sediment transport mechanisms, and bed evolution are more complex than in straight channels, owing to the interaction between the centrifugal force and the pressure gradient, which results in the formation of secondary currents. Therefore, using an appropriate numerical model that considers this fully three-dimensional effect, and subsequently, the model calibration are substantial tasks for achieving reliable simulation results. The calibration of numerical models as a subjective approach can become challenging and highly time-consuming, especially for inexperienced modelers, due to dealing with a large number of input parameters with respect to hydraulics and sediment transport. Using optimization methods can notably facilitate and expedite the calibration procedure by reducing the user intervention, which results in a more objective selection of parameters. This study focuses on the application of four different optimization algorithms for calibration of a 3D morphodynamic numerical model of a curved channel. The performance of a local gradient-based method is compared with three global optimization algorithms in terms of accuracy and computational time (model runs). The outputs of the optimization methods demonstrate similar sets of calibrated parameters and almost the same degree of accuracy according to the achieved minimum of the objective function. Accordingly, the most efficient method concerning the number of model runs (i.e., local optimization method) is selected for further investigation by setting up additional numerical models using different sediment transport formulae and various discharge rates. The comparisons of bed topography changes in several longitudinal and cross-sections between the measured data and the results of the calibrated numerical models are presented. The outcomes show an acceptable degree of accuracy for the automatically calibrated models.

A comparison of numerical methods for optimizing even aged stand management

1990 ◽  
Vol 20 (7) ◽  
pp. 961-969 ◽  
Author(s):  
Lauri T. Valsta
Keyword(s):  
Dynamic Programming ◽  
Species Composition ◽  
Random Search ◽  
Optimization Methods ◽  
Global Optimum ◽  
Computational Effort ◽  
Direct Search ◽  
Computational Time ◽  
Discrete State ◽  
Stand Management

A two-species, whole-stand, deterministic growth model was combined with three optimization methods to derive management regimes for species composition, thinnings, and rotation age, with the objective of maximizing soil expectation value. The methods compared were discrete time – discrete state dynamic programming, direct search using the Hooke and Jeeves algorithm, and random search. Optimum solutions for each of the methods varied considerably, required unequal amounts of computational time, and were not equally stable. Dynamic programming located global optimal solutions but did not determine them accurately, owing to discretized state space. Direct search yielded the largest objective function values with comparable computational effort, although the likelihood of finding a global optimum solution was high only for smaller problems with up to two or three thinnings during the rotation. Random search solutions varied considerably with regard to growing stock level and species composition and did not define a consistent management guideline. In general, direct search and dynamic programming appeared to be superior to random search.

scholarly journals APPLICATION OF GLOBAL OPTIMIZATION TO PREDICT STRAINS IN RC COMPRESSED COLUMNS

2021 ◽  
Vol 61 (1) ◽  
pp. 242-252
Author(s):  
Marek Lechman ◽  
Andrzej Stachurski
Keyword(s):  
Least Squares Method ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Trust Region ◽  
Global Solutions ◽  
Optimization Methods ◽  
Box Constraints ◽  
Particle Swarm Method ◽  
Global And Local Optimization ◽  
Global And Local

In this paper, the results of an application of global and local optimization methods to solve a problem of determination of strains in RC compressed structure members are presented. Solutions of appropriate sets of nonlinear equations in the presence of box constraints have to be found. The use of the least squares method leads to finding global solutions of optimization problems with box constraints. Numerical examples illustrate the effects of the loading value and the loading eccentricity on the strains in concrete and reinforcing steel in the a cross-section.Three different minimization methods were applied to compute them: trust region reflective, genetic algorithm tailored to problems with real double variables and particle swarm method. Numerical results on practical data are presented. In some cases, several solutions were found. Their existence has been detected by the local search with multistart, while the genetic and particle swarm methods failed to recognize their presence.

scholarly journals Prediction and analysis of penetration rate in drilling operation using deterministic and metaheuristic optimization methods

2021 ◽  
Author(s):  
Ibrahim Sobhi ◽  
Abdelmadjid Dobbi ◽  
Oussama Hachana
Keyword(s):  
High Performance ◽  
Mean Squared Error ◽  
Optimization Methods ◽  
Optimization Techniques ◽  
Computational Time ◽  
Objective Functions ◽  
Memory Space ◽  
Drilling Operation ◽  
Drilling Parameters ◽  
Selection Of

AbstractThe rate of penetration (ROP) optimization is one of the most important factors in improving drilling efficiency, especially in the downturn time of oil prices. This process is crucial in the well planning and exploration phases, where the selection of the drilling bits and parameters has a significant impact on the total cost and time of the drilling operation. Thus, the optimization and best selection of the drilling parameters are critical. Optimization of ROP is difficult due to the complexity of the relationship between the drilling variables and the ROP. For this reason, the development of high-performance computer systems, predictive models, and algorithms will be the best solution. In this study, a new investigation approach for ROP optimization has been done regarding different ROP models (Maurer, Bingham, Bourgoyne and Young models), algorithms (Multiple regression, ant colony optimization (ACO), fminunc, fminsearch, fsolve, lsqcurvefit, lsqnonlin), and different objective functions. The well-known data from the Louisiana field in an offshore well have been used to compare the used parameter estimation approach with other techniques. Indeed, datasets from an onshore well in the Hassi Messaoud Algerian field are explored. The results confirmed the superiority and the effectiveness of B&Y models compared to Bingham and Maurer models. Fminsearch, lsqcurvefit, ACO, and Excel (GRG) algorithms give the best results in ROP prediction while the application of the MNLR approach. Using the mean squared error (MSE) and the determination coefficient (R$$^{2}$$ 2 ) as objective functions significantly increases the accuracy prediction where the results given are ($$R=0.9522$$ R = 0.9522 , $$RMSE=2.85$$ R M S E = 2.85 ) and ($$R= 0.9811$$ R = 0.9811 , $$RMSE=4.08$$ R M S E = 4.08 ) for Wells 1 and 2, respectively. This study validates the application of B&Y model in both onshore and offshore wells. The findings reveal to deal with data limitation problems in ROP prediction. Simple and effective optimization techniques that require less memory space and computational time have been provided.

scholarly journals Harmonic Elimination of Cascaded Multilevel Inverter using Metaheuristic Optimization Methods

2018 ◽  
Vol 7 (4.15) ◽  
pp. 272 ◽  
Author(s):  
Srikanta Kumar Dash ◽  
Byamakesh Nayak ◽  
Jiban Ballav Sahu ◽  
Rojalin Rout
Keyword(s):  
Harmonic Distortion ◽  
Optimization Methods ◽  
Optimization Method ◽  
Multilevel Inverter ◽  
Computational Time ◽  
Local Minima ◽  
Metaheuristic Optimization ◽  
Harmonic Elimination ◽  
Whale Optimization ◽  
Cascaded Multilevel Inverter

The harmonic elimination of multilevel inverters is a complicated task that includes nonlinear transcendental equations. With the increase in the level of the multilevel inverter, the no of variables of the equation also increases which makes the problem more complicated. Metaheuristic optimization algorithms play an important role in finding out optimum switching angles required for elimination of harmonics in a lesser computational time avoiding multiple local minima. This paper deals with the harmonic elimination of cascaded multilevel inverter using whale optimization algorithm. The whale optimization method has the ability to escape local minima and it takes less time of computation of results. Results are verified theoretically by taking an example of a 15-level cascaded H-bridge inverter fed from equal d.c.sources. The above scheme well minimizes lower order harmonics and gives better output voltage and a low total harmonic distortion.  

scholarly journals Design and Optimization of Capacitated Supply Chain Networks Including Quality Measures

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Krystel K. Castillo-Villar ◽  
Neale R. Smith ◽  
José F. Herbert-Acero
Keyword(s):  
Supply Chain ◽  
Network Design ◽  
Optimization Methods ◽  
Mixed Integer ◽  
Computational Time ◽  
Quality Level ◽  
Supply Chain Network Design ◽  
Supply Chain Network ◽  
Quality Costs ◽  
Business Entities

This paper presents (1) a novel capacitated model for supply chain network design which considers manufacturing, distribution, and quality costs (named SCND-COQ model) and (2) five combinatorial optimization methods, based on nonlinear optimization, heuristic, and metaheuristic approaches, which are used to solve realistic instances of practical size. The SCND-COQ model is a mixed-integer nonlinear problem which can be used at a strategic planning level to design a supply chain network that maximizes the total profit subject to meeting an overall quality level of the final product at minimum costs. The SCND-COQ model computes the quality-related costs for the whole supply chain network considering the interdependencies among business entities. The effectiveness of the proposed solution approaches is shown using numerical experiments. These methods allow solving more realistic (capacitated) supply chain network design problems including quality-related costs (inspections, rework, opportunity costs, and others) within a reasonable computational time.

scholarly journals Implementable tensor methods in unconstrained convex optimization

2019 ◽  
Author(s):  
Yurii Nesterov
Keyword(s):  
Convex Optimization ◽  
Auxiliary Problem ◽  
Computational Cost ◽  
Rates Of Convergence ◽  
Smoothness Condition ◽  
Third Order ◽  
Worst Case ◽  
Complexity Bounds ◽  
The Third ◽  
Tensor Methods

AbstractIn this paper we develop new tensor methods for unconstrained convex optimization, which solve at each iteration an auxiliary problem of minimizing convex multivariate polynomial. We analyze the simplest scheme, based on minimization of a regularized local model of the objective function, and its accelerated version obtained in the framework of estimating sequences. Their rates of convergence are compared with the worst-case lower complexity bounds for corresponding problem classes. Finally, for the third-order methods, we suggest an efficient technique for solving the auxiliary problem, which is based on the recently developed relative smoothness condition (Bauschke et al. in Math Oper Res 42:330–348, 2017; Lu et al. in SIOPT 28(1):333–354, 2018). With this elaboration, the third-order methods become implementable and very fast. The rate of convergence in terms of the function value for the accelerated third-order scheme reaches the level $$O\left( {1 \over k^4}\right) $$O1k4, where k is the number of iterations. This is very close to the lower bound of the order $$O\left( {1 \over k^5}\right) $$O1k5, which is also justified in this paper. At the same time, in many important cases the computational cost of one iteration of this method remains on the level typical for the second-order methods.

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