Structure of the first-order solution set for a class of nonlinear programs with parameters

1986 ◽  
Vol 34 (1) ◽  
pp. 84-110 ◽  
Author(s):  
Stephen Schecter
Keyword(s):  
Solution Set ◽  
First Order ◽  
Nonlinear Programs ◽  
Order Solution

Radiant Heat Transfer From Isothermal Dispersions With Isotropic Scattering

1967 ◽  
Vol 89 (4) ◽  
pp. 300-308 ◽  
Author(s):  
R. H. Edwards ◽  
R. P. Bobco
Keyword(s):  
Heat Transfer ◽  
Approximate Solutions ◽  
Radiant Heat ◽  
Second Order ◽  
Isotropic Scattering ◽  
Radiant Heat Transfer ◽  
Approximate Methods ◽  
First Order ◽  
Order Solution ◽  
Radiant Transfer

Two approximate methods are presented for making radiant heat-transfer computations from gray, isothermal dispersions which absorb, emit, and scatter isotropically. The integrodifferential equation of radiant transfer is solved using moment techniques to obtain a first-order solution. A second-order solution is found by iteration. The approximate solutions are compared to exact solutions found in the literature of astrophysics for the case of a plane-parallel geometry. The exact and approximate solutions are both expressed in terms of directional and hemispherical emissivities at a boundary. The comparison for a slab, which is neither optically thin nor thick (τ = 1), indicates that the second-order solution is accurate to within 10 percent for both directional and hemispherical properties. These results suggest that relatively simple techniques may be used to make design computations for more complex geometries and boundary conditions.

SEMI-ANALYTIC FIRST-ORDER SOLUTION FOR OPTIMAL LOW-THRUST TRAJECTORIES AROUND MOON

2021 ◽  
Author(s):  
Sandro da Silva Fernandes ◽  
Luiz Arthur Gagg Filho
Keyword(s):  
Low Thrust ◽  
First Order ◽  
Order Solution

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 Aanalytical Solution for Motion Around Radiated Varying Mass Body

2019 ◽  
Vol 16 ◽  
pp. 8407-8419
Author(s):  
Marwa Abdullah Bin Humaidan ◽  
M. I. El-Saftawy ◽  
H. M. Asiri
Keyword(s):  
Time Series ◽  
Radiation Pressure ◽  
Pressure Effect ◽  
Hamiltonian Function ◽  
Perturbation Techniques ◽  
First Order ◽  
D Operator ◽  
Order Solution ◽  
Delaunay Variables ◽  
Varying Mass

In this work we will add the radiation pressure effect of varying mass body to the model of varying mass Hamiltonian function, including Periastron effect. The problem was formulated in terms of Delaunay variables. The solution of the problem was constructed based on Delava – Hansilmair perturbation techniques. Finally we find the first order solution for the problem as time series by calculating the desired order for the D operator and variables.

scholarly journals Lie transforms and motion of a charged particle in a periodic magnetic field

1984 ◽  
Vol 7 (1) ◽  
pp. 159-169
Author(s):  
Sikha Bhattacharyya ◽  
R. K. Roy Choudhury
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Averaging Method ◽  
Second Order ◽  
Lie Series ◽  
Periodic Magnetic Field ◽  
First Order ◽  
Order Solution ◽  
Lie Transforms ◽  
Spatially Periodic

We use the Lie series averaging method to obtain a complete second order solution for motion of a charged particle in a spatially periodic magnetic field. A comparison is made with the first order solution obtained previously by Coffey.

Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow

1974 ◽  
Vol 25 (1) ◽  
pp. 59-68 ◽  
Author(s):  
W H Hui ◽  
J Hamilton
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Power Series ◽  
Unsteady Flow ◽  
The Body ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Method Of Solution

SummaryThe problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.

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