First Order Constraint Qualifications

2012 ◽  
Keyword(s):  
Constraint Qualifications ◽  
First Order ◽  
Order Constraint

scholarly journals Notes on Constraint Qualifications for Second-Order Optimality Conditions

2019 ◽  
Vol 11 (5) ◽  
pp. 16
Author(s):  
Giorgio Giorgi
Keyword(s):  
Optimality Conditions ◽  
Constraint Qualification ◽  
Constraint Qualifications ◽  
Second Order ◽  
Necessary Optimality Condition ◽  
First Order ◽  
Second Order Optimality Conditions ◽  
Order Constraint ◽  
Local Approximations ◽  
Abadie Constraint Qualification

In the first part of this paper we point out some basic properties of the critical cones used in second-order optimality conditions and give a simple proof of a strong second-order necessary optimality condition by assuming a “modified” first-order Abadie constraint qualification. In the second part we give some insights on second-order constraint qualifications related to second-order local approximations of the feasible set.

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Nonlinear Programs ◽  
Mathematical Programs ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.

scholarly journals Theory of finite or infinite trees revisited

2008 ◽  
Vol 8 (04) ◽  
pp. 431-489 ◽  
Author(s):  
KHALIL DJELLOUL ◽  
THI-BICH-HANH DAO ◽  
THOM FRÜHWIRTH
Keyword(s):  
Constraint Satisfaction ◽  
Decision Procedure ◽  
Constraint Satisfaction Problem ◽  
Free Variable ◽  
Constraint Solver ◽  
First Order ◽  
Infinite Trees ◽  
Order Constraint ◽  
Infinite Set ◽  
Rewriting Rules

AbstractWe present in this paper a first-order axiomatization of an extended theoryTof finite or infinite trees, built on a signature containing an infinite set of function symbols and a relationfinite(t), which enables to distinguish between finite and infinite trees. We show thatThas at least one model and prove its completeness by giving not only a decision procedure, but a full first-order constraint solver that gives clear and explicit solutions for any first-order constraint satisfaction problem inT. The solver is given in the form of 16 rewriting rules that transform any first-order constraintinto an equivalent disjunction φ of simple formulas such that φ is either the formulatrueor the formulafalseor a formula having at least one free variable, being equivalent neither totruenor tofalseand where the solutions of the free variables are expressed in a clear and explicit way. The correctness of our rules implies the completeness ofT. We also describe an implementation of our algorithm in CHR (Constraint Handling Rules) and compare the performance with an implementation in C++ and that of a recent decision procedure for decomposable theories.

Experimental analysis on mechanical properties of BF/PLA composites and its lightweight design on power battery box

2021 ◽  
pp. 095440702110658
Author(s):  
Ying Zhao ◽  
Siqi Zheng ◽  
Minghan Yan ◽  
Xuanming Liu ◽  
Binlin Wang ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Working Conditions ◽  
Lightweight Design ◽  
Mechanical Shock ◽  
First Order ◽  
Automotive Components ◽  
Power Battery ◽  
Element Simulation ◽  
Order Constraint ◽  
Modal Vibration

In response to the concept of energy conservation and environmental protection, a novel composite battery box with BF/PLA composite is proposed. Firstly, the mechanical properties of BF/PLA composite are tested, and it is concluded that the property parameters of BF/PLA composite with 50% BF mass fraction is selected as the material property parameter of subsequent finite element simulation. Subsequently, the statics analysis and constraint modal analysis of the traditional metal battery box are carried out under the typical working conditions of rapid turning and braking under vertical bumping. Based on this, the upper and lower box materials of the battery box except the bracket are replaced by BF/PLA composite. The morphology optimization, topology optimization and free size optimization are carried out with the constraint that the first-order modal vibration frequency is no less than 30 Hz. Compared with the traditional metal battery box, the stiffness and strength of the optimized BF/PLA composite battery box are significantly enhanced. Moreover, the first-order constraint modal frequency increases by 15.5%, and the comprehensive weight reduction ratio reaches 40.88%. Finally, the optimized BF/PLA composite battery box is verified under random vibration, mechanical shock analysis, collision analysis, extrusion and falling ball analysis and drop analysis conditions. Meanwhile, compared with the traditional metal battery box under the same working conditions, the excellent reliability of the composite battery box is highlighted. The proposed BF/PLA composite battery box satisfies the requirements of stiffness and strength performances under various working conditions, which provides theoretical and data support for the application of composite materials in battery box and other automotive components.

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