Global Solution of Optimization Problems with Dynamic Systems Embedded

2004 ◽  
pp. 477-497 ◽  
Author(s):  
A. B. Singer ◽  
P. I. Barton
Keyword(s):  
Global Solution ◽  
Dynamic Systems ◽  
Optimization Problems

Smoothing Approximation to the New Exact Penalty Function with Two Parameters

2021 ◽  
pp. 2140010
Author(s):  
Jing Qiu ◽  
Jiguo Yu ◽  
Shujun Lian
Keyword(s):  
Global Solution ◽  
Penalty Function ◽  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Exact Penalty ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Nonlinear Inequality ◽  
Two Parameters

In this paper, we propose a new non-smooth penalty function with two parameters for nonlinear inequality constrained optimization problems. And we propose a twice continuously differentiable function which is smoothing approximation to the non-smooth penalty function and define the corresponding smoothed penalty problem. A global solution of the smoothed penalty problem is proved to be an approximation global solution of the non-smooth penalty problem. Based on the smoothed penalty function, we develop an algorithm and prove that the sequence generated by the algorithm can converge to the optimal solution of the original problem.

scholarly journals Perspective Solutions for the Design of Drilling Tools

2019 ◽  
Vol 105 ◽  
pp. 03027 ◽  
Author(s):  
Ulugbek Mannanov ◽  
Javokhir Toshov ◽  
Lazizjon Toshniyozov
Keyword(s):  
Energy Consumption ◽  
Dynamic Systems ◽  
Optimization Problems ◽  
Bottom Hole ◽  
Drill Bits ◽  
Drilling Tools

The article considers the ways to solve optimization problems of drill bits on a deterministic basis through studying and using the “Regularity of energy consumption of dynamic systems from resistance to motion forces”, which directly indicates the causes of bit balling formation, the reasons for the insufficient stability of the bearing assemblies of the cones, the causes of instability of the drill bits at the bottom of the well. Theoretical grounded search was done to use certain methods for designing drill bits of cutting-abrasive type, working in the rotational steam mode, which determine uniform wear of armaments for all crowns of working matrices and uniform destruction of the rock through all of the annular bottom hole.

Global Solution of Optimization Problems in Rotorcraft Flight Mechanics

2015 ◽  
Vol 28 (1) ◽  
pp. 04014042 ◽  
Author(s):  
Carlo L. Bottasso ◽  
Fabio Luraghi ◽  
Giorgio Maisano ◽  
Meng Shaohua
Keyword(s):  
Global Solution ◽  
Optimization Problems ◽  
Flight Mechanics

scholarly journals Understanding measure-driven algorithms solving irreversibly ill-conditioned problems

2021 ◽  
Author(s):  
Jakub Sawicki ◽  
Marcin Łoś ◽  
Maciej Smołka ◽  
Robert Schaefer
Keyword(s):  
Global Optimization ◽  
Markov Chain ◽  
Dynamic Systems ◽  
Positive Measure ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Real Life ◽  
Population Based ◽  
Ergodic Markov Chain ◽  
Markov Chain Models

AbstractThe paper helps to understand the essence of stochastic population-based searches that solve ill-conditioned global optimization problems. This condition manifests itself by presence of lowlands, i.e., connected subsets of minimizers of positive measure, and inability to regularize the problem. We show a convenient way to analyze such search strategies as dynamic systems that transform the sampling measure. We can draw informative conclusions for a class of strategies with a focusing heuristic. For this class we can evaluate the amount of information about the problem that can be gathered and suggest ways to verify stopping conditions. Next, we show the Hierarchic Memetic Strategy coupled with Multi-Winner Evolutionary Algorithm (HMS/MWEA) that follow the ideas from the first part of the paper. We introduce a complex, ergodic Markov chain of their dynamics and prove an asymptotic guarantee of success. Finally, we present numerical solutions to ill-conditioned problems: two benchmarks and a real-life engineering one, which show the strategy in action. The paper recalls and synthesizes some results already published by authors, drawing new qualitative conclusions. The totally new parts are Markov chain models of the HMS structure of demes and of the MWEA component, as well as the theorem of their ergodicity.

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