scholarly journals On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 465
Author(s):  
Agnieszka Prusińska ◽  
Krzysztof Szkatuła ◽  
Alexey Tret’yakov
Keyword(s):  
Computational Complexity ◽  
Polynomial Complexity ◽  
Initial Point ◽  
Quadratic Functions ◽  
Problem Dimension ◽  
Piecewise Quadratic Functions ◽  
Large Systems ◽  
Systems Of Linear Inequalities ◽  
Number Of Iterations ◽  
Finite Number Of Iterations

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.

A polynomial algorithm for the quadratic programming problem

2014 ◽  
Vol 29 (3) ◽  
Author(s):  
Valentin A. Bereznev
Keyword(s):  
Computational Complexity ◽  
Quadratic Form ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Polynomial Complexity ◽  
Polynomial Algorithm ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Quadratic Programming Problem ◽  
Convex Polyhedral Cone

AbstractAn approach based on projection of a vector onto a pointed convex polyhedral cone is proposed for solving the quadratic programming problem with a positive definite matrix of the quadratic form. It is proved that this method has polynomial complexity. A method is said to be of polynomial computational complexity if the solution to the problem can be obtained in N

Initial Design Strategies for Iterative Design

1990 ◽  
Author(s):  
Natarajan Ramachandran ◽  
Noshir A. Langrana ◽  
Louis Steinberg
Keyword(s):  
Initial Point ◽  
Design Methods ◽  
Design Strategies ◽  
Iterative Design ◽  
Initial Design ◽  
Iterative Model ◽  
Starting Point ◽  
Time Required ◽  
Initial Starting ◽  
Number Of Iterations

Abstract This paper discusses methods to retrieve design(s) from a design library in order to achieve a better initial starting point for the iterative model of the design process. The motivation for doing this is to reduce the extensive analysis time required for many iterative design problems. Starting a design at a favorable initial point should help reduce the number of iterations. Four initial design methods have been investigated varying from a simple non-library method to methods that use designs from a library. To evaluate the effectiveness of these methods, the initial design methods were tested on four example problems. They are, a cantilever beam, a gear-pair, a v-belt and an extruder-die. It was found that the number of iterations reduced approximately as 1/n, where n is the number of stored values in the design library.

Partially doubly symmetric solutions of general Sylvester matrix equations

2019 ◽  
Vol 42 (3) ◽  
pp. 503-517
Author(s):  
Masoud Hajarian
Keyword(s):  
Control Systems ◽  
Linear Matrix ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Sylvester Matrix ◽  
Sylvester Matrix Equations ◽  
Linear Matrix Equations ◽  
Scientific Fields ◽  
Number Of Iterations ◽  
Finite Number Of Iterations

The study of linear matrix equations is extremely important in many scientific fields such as control systems and stability analysis. In this work, we aim to design the Hestenes-Stiefel (HS) version of biconjugate residual (Bi-CR) algorithm for computing the (least Frobenius norm) partially doubly symmetric solution [Formula: see text] of the general Sylvester matrix equations [Formula: see text] for [Formula: see text]. We show that the proposed algorithm converges in a finite number of iterations. Finally, numerical results compare the proposed algorithm to alternative algorithms.

Solving Large-Scale Multipoint Lighting Design Problem Using Multi-Agent Environment

2011 ◽  
Vol 486 ◽  
pp. 179-182 ◽  
Author(s):  
Adam Sędziwy ◽  
Leszek Kotulski
Keyword(s):  
Computational Complexity ◽  
Design Process ◽  
Large Scale ◽  
Lighting Design ◽  
The Other ◽  
Economic Issues ◽  
Computational Environment ◽  
Multi Agent ◽  
Design Requirements ◽  
Large Systems

In the paper we focus on the problem of large-scale distribution of lighting points. Its solution is constrained by economic issues like power consumption or exploitation costs and, on the other side, by the computational complexity of design process. Multi-agent computational environment combined with graph and hypergraph representations of a problem allow meeting design requirements and objectives and, on the other hand, make the method applicable for large systems for which computational effectiveness is a crucial factor.

ADAPTIVE LEAST SQUARES ACQUISITION OF HIGH RESOLUTION IMAGES

2005 ◽  
Vol 02 (01) ◽  
pp. 45-53 ◽  
Author(s):  
S. E. EL-KHAMY ◽  
M. M. HADHOUD ◽  
M. I. DESSOUKY ◽  
B. M. SALAM ◽  
F. E. ABD EL-SAMIE
Keyword(s):  
Computational Complexity ◽  
High Resolution ◽  
Least Squares ◽  
Edge Effects ◽  
Estimation Error ◽  
Point Of View ◽  
Suggested Algorithm ◽  
High Resolution Images ◽  
Number Of Iterations ◽  
Least Squares Approach

This paper presents a least squares block by block adaptive approach for the acquisition of high resolution (HR) images from available (LR) images. The suggested algorithm is based on the segmentation of the image to overlapping blocks and the interpolation of each block separately. The purpose of the overlapping of blocks is to avoid edge effects. An adaptive 2D least squares approach, which considers the image acquisition model, is used in the minimization of the estimation error of each block. In this suggested algorithm, a weight matrix of moderate dimensions is estimated in a small number of iterations to interpolate each block. This algorithm avoids the large computational complexity due to the matrices of large dimensions required to interpolate the image as a whole. The performance of the proposed algorithm is studied for different LR images with different SNRs. The performance of the proposed algorithm is also compared to the standard as well as the warped distance cubic O-MOMS image interpolation algorithms from the PSNR point of view.

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