Hölder behavior of optimal solutions and directional differentiability of marginal functions in nonlinear programming

1996 ◽  
Vol 90 (3) ◽  
pp. 555-580 ◽  
Author(s):  
L. I. Minchenko ◽  
P. P. Sakolchik
Keyword(s):  
Nonlinear Programming ◽  
Optimal Solutions ◽  
Directional Differentiability ◽  
Marginal Functions

Iterative Fixture Layout and Clamping Force Optimization Using the Genetic Algorithm

2001 ◽  
Vol 124 (1) ◽  
pp. 119-125 ◽  
Author(s):  
Krishnakumar Kulankara ◽  
Srinath Satyanarayana ◽  
Shreyes N. Melkote
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Programming ◽  
Primary Objective ◽  
Fixture Design ◽  
Clamping Force ◽  
Optimal Solutions ◽  
Fixture Layout ◽  
Force Optimization ◽  
Nonlinear Programming Methods ◽  
Objective Being

Fixture design is a critical step in machining. An important aspect of fixture design is the optimization of the fixture, the primary objective being the minimization of workpiece deflection by suitably varying the layout of fixture elements and the clamping forces. Previous methods for fixture design optimization have treated fixture layout and clamping force optimization independently and/or used nonlinear programming methods that yield sub-optimal solutions. This paper deals with application of the genetic algorithm (GA) for fixture layout and clamping force optimization for a compliant workpiece. An iterative algorithm that minimizes the workpiece elastic deformation for the entire cutting process by alternatively varying the fixture layout and clamping force is proposed. It is shown via an example of milling fixture design that this algorithm yields a design that is superior to the result obtained from either fixture layout or clamping force optimization alone.

An improved formulation for optimizing rocker-bogie suspension rover for climbing steps

2019 ◽  
Vol 233 (18) ◽  
pp. 6538-6558 ◽  
Author(s):  
Sam Noble ◽  
K Kurien Issac
Keyword(s):  
Nonlinear Programming ◽  
Optimal Design ◽  
Local Minimum ◽  
Single Step ◽  
Optimal Solutions ◽  
Performance Parameters ◽  
Smooth Functions ◽  
Gradient Based ◽  
Wheel Radius ◽  
Better Than

We address the problem of improving mobility of rovers with rocker-bogie suspension. Friction and torque requirements for climbing a single step were considered as performance parameters. The main contribution of the paper is an improved formulation for rover optimization using smooth functions, which enables use of powerful gradient based nonlinear programming (NLP) solvers for finding solutions. Our formulation does not have certain shortcomings present in some earlier formulations. We first formulate the problem of determining optimal torques to be applied to the wheels to minimize (a) friction requirement, and (b) torque requirement, and obtain demonstrably optimal solutions. We then formulate the problem of optimal design of the rover itself. Our solution for climbing a step of height two times the wheel radius is 13% better than that of the nominal rover. This solution is verified to be a local minimum by checking Karush–Kuhn–Tucker conditions. Optimal solutions were obtained for both forward and backward climbing. We show that some earlier formulations cannot obtain optimal solutions in certain situations. We also obtained optimal design for climbing steps of three different heights, with a friction requirement which is 15% lower than that of the nominal rover.

scholarly journals Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM

2016 ◽  
Vol 6 (2) ◽  
pp. 75-83 ◽  
Author(s):  
Firat Evirgen
Keyword(s):  
Nonlinear Programming ◽  
Fractional Order ◽  
Optimization Problems ◽  
Variational Iteration Method ◽  
Optimal Solutions ◽  
Order Model ◽  
Fractional Order Differential Equations ◽  
Runge Kutta Method ◽  
Fractional Order Model ◽  
Gradient Based

In this paper, a class of Nonlinear Programming problem is modeled with gradient based system of fractional order differential equations in Caputo's sense. To see the overlap between the equilibrium point of the fractional order dynamic system and theoptimal solution of the NLP problem in a longer timespan the Multistage Variational ?teration Method isapplied. The comparisons among the multistage variational iteration method, the variationaliteration method and the fourth order Runge-Kutta method in fractional and integer order showthat fractional order model and techniques can be seen as an effective and reliable tool for finding optimal solutions of Nonlinear Programming problems.

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