Contingent cone to a set defined by equality and inequality constraints at a Fréchet differentiable point

1994 ◽  
Vol 81 (3) ◽  
pp. 469-478 ◽  
Author(s):  
S. Di ◽  
R. Poliquin
Keyword(s):  
Inequality Constraints ◽  
Contingent Cone ◽  
Equality And Inequality Constraints ◽  
Fréchet Differentiable

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.

A Comparative Study of Improved Teaching Learning Based Optimization Technique on Economic Load Dispatch Problem with Generator Constraints

2016 ◽  
Vol 5 (4) ◽  
pp. 1-25 ◽  
Author(s):  
Sumit Banerjee ◽  
Chandan Chanda ◽  
Deblina Maity
Keyword(s):  
Optimization Technique ◽  
Inequality Constraints ◽  
Test System ◽  
Economic Load Dispatch ◽  
Thermal Plant ◽  
Equality And Inequality Constraints ◽  
Teaching Learning Based Optimization ◽  
Teaching Learning ◽  
Operational Constraints ◽  
Rate Limit

This article presents a novel improved teaching learning based optimization (I-TLBO) technique to solve economic load dispatch (ELD) problem of the thermal plant without considering transmission losses. The proposed methodology can take care of ELD problems considering practical nonlinearities such as ramp rate limit, prohibited operating zone and valve point loading. The objective of economic load dispatch is to determine the optimal power generation of the units to meet the load demand, such that the overall cost of generation is minimized, while satisfying different operational constraints. I-TLBO is a recently developed evolutionary algorithm based on two basic concepts of education namely teaching phase and learning phase. The effectiveness of the proposed algorithm has been verified on test system with equality and inequality constraints. Compared with the other existing techniques demonstrates the superiority of the proposed algorithm.

A Study of Airline Fuel Planning Optimization Using R-Ga

2020 ◽  
Vol 46 ◽  
pp. 189-197
Author(s):  
Ekene Gabriel Okafor ◽  
Osaretin Kole Uhuegho ◽  
Christopher Manshop ◽  
Paul Olugbeji Jemitola ◽  
Osichinaka Chiedu Ubadike
Keyword(s):  
Regression Analysis ◽  
Fuel Consumption ◽  
Large Time ◽  
Inequality Constraints ◽  
Flight Time ◽  
Planning Problem ◽  
Study Objective ◽  
Planning Optimization ◽  
Equality And Inequality Constraints ◽  
Human Effort

In this study, airline planning optimization problem based on ferry strategy was considered. Cost was the study objective function subject to forty equality and inequality constraints. Regression analysis as well a genetic algorithm (GA) was used to solve the problem. The mathematical relationship between flight fuel consumption and flight time was established using regression analysis, while GA was used for the optimization. The established mathematical model was used to predict the fuel consumption for the twenty scheduled flight consider based on their respective flight time. The result was found to be satisfactory, as optimal fuel lift plan was achieved in approximately twenty seconds of program run time, as against the large time usually spend using human effort to solve the fuel planning problem. The optimized fuel lift plan was compared with the actual fuel lift plan executed by the airline for the twenty scheduled flight considered. The result revealed thirty percent savings using the optimized plan in comparison to the actual fuel lift plan executed by the airline.

Combined Analysis and Optimization of Extended Heat Transfer Surfaces

1985 ◽  
Vol 107 (3) ◽  
pp. 527-532 ◽  
Author(s):  
A. N. Hrymak ◽  
G. J. McRae ◽  
A. W. Westerberg
Keyword(s):  
Optimization Problem ◽  
Radiative Heat ◽  
Inequality Constraints ◽  
Finite Element Approximation ◽  
Problem Formulation ◽  
Element Approximation ◽  
Problem Solution ◽  
Radiative Heat Loss ◽  
Equality And Inequality Constraints ◽  
Grid Points

This study presents an efficient numerical method to discover the optimal shape for a fin subject to both convective and radiative heat loss. Problem formulation is a finite element approximation to the conduction equation embedded within and solved simultaneously with the shape optimization problem. The approach handles arbitrary equality and inequality constraints. Grid points move to conform to the fin shape during the problem solution, reducing the number of elements required in the solution.

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