Solving Nonconvex Optimization Problems in Systems and Control: A Polynomial B-spline Approach

被引：2

作者：

Gawali, Deepak ^{[1
,3
]}

Zidna, Ahmed ^{[2
]}

Nataraj, Paluri S. V. ^{[3
]}

机构：

[1] Vidyavardhinis Coll Engn & Technol, Vasai, Maharashtra, India

[2] Univ Lorraine, Theoret & Appl Comp Sci Lab, Nancy, France

[3] Indian Inst Technol, Syst & Control Engn, Bombay, Maharashtra, India

来源：

MODELLING, COMPUTATION AND OPTIMIZATION IN INFORMATION SYSTEMS AND MANAGEMENT SCIENCES - MCO 2015, PT 1 | 2015年 / 359卷

关键词：

Polynomial B-spline; Global optimization; Polynomial optimization; Constrained optimization; GLOBAL OPTIMIZATION; RANGE;

D O I：

10.1007/978-3-319-18161-5_40

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Many problems in systems and control engineering can be formulated as constrained optimization problems with multivariate polynomial objective functions. We propose algorithms based on polynomial B-spline form for constrained global optimization of multivariate polynomial functions. The proposed algorithms are based on a branch-and-bound framework. We tested the proposed basic constrained global optimization algorithms by considering three test problems from systems and control. The obtained results agree with those reported in literature.

引用

页码：467 / 478

页数：12

共 23 条

[1] [Anonymous], 2012, MATLAB VERS 8 0 0 78
[2] [Anonymous], 1996, Rigorous global search: continuous problems. Nonconvex optimization and its applications
[3] Solving quadratic distance problems: An LMI-based approach
Chesi, G
Garulli, A
Tesi, A
Vicino, A
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2003, 48 (02) : 200 - 212
[4] An LMI approach to constrained optimization with homogeneous forms
Chesi, G
Tesi, A
Vicino, A
Genesio, R
[J]. SYSTEMS & CONTROL LETTERS, 2001, 42 (01) : 11 - 19
[5] Estimating the domain of attraction via union of continuous families of Lyapunov estimates
Chesi, Graziano
[J]. SYSTEMS & CONTROL LETTERS, 2007, 56 (04) : 326 - 333
[6] DeVore R. A., 1993, Grundlehren der Mathematischen Wissenschaften, V303
[7] Floudas C.A., 1999, Handbook of Test Problems in Local and Global Optimization
[8] Hansen E., 2003, Global Optimization Using Interval Analysis: Revised and Expanded, V264
[9] Solving nonconvex optimization problems
Henrion, D
Lasserre, JB
[J]. IEEE CONTROL SYSTEMS MAGAZINE, 2004, 24 (03): : 72 - 83
[10] Horst R., 1995, Handbook of Global Optimization: Nonconvex Optimization and Its Application

← 1 2 3 →