Convex and Concave Relaxations for the Parametric Solutions of Semi-explicit Index-One Differential-Algebraic Equations

被引：12

作者：

Scott, Joseph K. ^{[1
]}

Barton, Paul I. ^{[1
]}

机构：

[1] MIT, Dept Chem Engn, Proc Syst Engn Lab, Cambridge, MA 02139 USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2013年 / 156卷 / 03期

基金：

美国国家科学基金会;

关键词：

Dynamic optimization; Optimal control; Global optimization; Differential-algebraic equations; Convex relaxation; DETERMINISTIC GLOBAL OPTIMIZATION; DYNAMIC OPTIMIZATION; CHEMICAL-KINETICS; SYSTEMS; ALGORITHMS; ODES;

D O I：

10.1007/s10957-012-0149-8

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

A method is presented for computing convex and concave relaxations of the parametric solutions of nonlinear, semi-explicit, index-one differential-algebraic equations (DAEs). These relaxations are central to the development of a deterministic global optimization algorithm for problems with DAEs embedded. The proposed method uses relaxations of the DAE equations to derive an auxiliary system of DAEs, the solutions of which are proven to provide the desired relaxations. The entire procedure is fully automatable.

引用

页码：617 / 649

页数：33

共 34 条

[1] Convex and Concave Relaxations for the Parametric Solutions of Semi-explicit Index-One Differential-Algebraic Equations
Joseph K. Scott
Paul I. Barton
Journal of Optimization Theory and Applications, 2013, 156 : 617 - 649
[2] On Koopman Operator Framework for Semi-explicit Differential-Algebraic Equations
Susuki, Yoshihiko
IFAC PAPERSONLINE, 2021, 54 (14): : 341 - 345
[3] Periodic solutions of semi-explicit differential-algebraic equations with time-dependent constraints
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BOUNDARY VALUE PROBLEMS, 2014, : 1 - 19
[4] Periodic solutions of semi-explicit differential-algebraic equations with time-dependent constraints
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Boundary Value Problems, 2014
[5] HALF-EXPLICIT RUNGE-KUTTA METHODS FOR SEMI-EXPLICIT DIFFERENTIAL-ALGEBRAIC EQUATIONS OF INDEX-1
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STREHMEL, K
WEINER, R
NUMERISCHE MATHEMATIK, 1993, 64 (04) : 409 - 431
[6] RUNGE-KUTTA METHODS FOR LINEAR SEMI-EXPLICIT OPERATOR DIFFERENTIAL-ALGEBRAIC EQUATIONS
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MATHEMATICS OF COMPUTATION, 2018, 87 (309) : 149 - 174
[7] Interval bounds on the solutions of semi-explicit index-one DAEs. Part 1: analysis
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Numerische Mathematik, 2013, 125 : 1 - 25
[8] Interval bounds on the solutions of semi-explicit index-one DAEs. Part 2: computation
Scott, Joseph K.
Barton, Paul I.
NUMERISCHE MATHEMATIK, 2013, 125 (01) : 27 - 60
[9] Interval bounds on the solutions of semi-explicit index-one DAEs. Part 2: computation
Joseph K. Scott
Paul I. Barton
Numerische Mathematik, 2013, 125 : 27 - 60
[10] Interval bounds on the solutions of semi-explicit index-one DAEs. Part 1: analysis
Scott, Joseph K.
Barton, Paul I.
NUMERISCHE MATHEMATIK, 2013, 125 (01) : 1 - 25

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