A Generalized Return Vector for Projection Methods in Optimization With Nonlinear Constraints

1976 ◽  
Vol 98 (3) ◽  
pp. 816-819
Author(s):  
K. T. A. Ho ◽  
M. A. Townsend
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Projection Methods ◽  
Feasible Region ◽  
Nonlinear Constraints ◽  
Variable Metric Methods ◽  
Variable Metric ◽  
Numerical Example ◽  
Constrained Nonlinear Optimization

Variable metric methods can be adapted to constrained nonlinear optimization by incorporating projection methods and a return vector when the indicated next step leaves the feasible region. A generalized return vector is developed here which yields a superior return to the feasible region in terms of the metric associated with the objective function. It is shown that a better point results and faster convergence is expected. A numerical example is given.

scholarly journals Research on the inverse kinematics of manipulator using an improved self-adaptive mutation differential evolution algorithm

2021 ◽  
Vol 18 (3) ◽  
pp. 172988142110144
Author(s):  
Qianqian Zhang ◽  
Daqing Wang ◽  
Lifu Gao
Keyword(s):  
Differential Evolution ◽  
Objective Function ◽  
Inverse Kinematics ◽  
Differential Evolution Algorithm ◽  
Weight Coefficient ◽  
Adaptive Mutation ◽  
Feasible Region ◽  
Serial Manipulators ◽  
De Algorithm ◽  
Self Adaptive

To assess the inverse kinematics (IK) of multiple degree-of-freedom (DOF) serial manipulators, this article proposes a method for solving the IK of manipulators using an improved self-adaptive mutation differential evolution (DE) algorithm. First, based on the self-adaptive DE algorithm, a new adaptive mutation operator and adaptive scaling factor are proposed to change the control parameters and differential strategy of the DE algorithm. Then, an error-related weight coefficient of the objective function is proposed to balance the weight of the position error and orientation error in the objective function. Finally, the proposed method is verified by the benchmark function, the 6-DOF and 7-DOF serial manipulator model. Experimental results show that the improvement of the algorithm and improved objective function can significantly improve the accuracy of the IK. For the specified points and random points in the feasible region, the proportion of accuracy meeting the specified requirements is increased by 22.5% and 28.7%, respectively.

scholarly journals An alternative perspective on copositive and convex relaxations of nonconvex quadratic programs

2021 ◽  
Author(s):  
E. Alper Yıldırım
Keyword(s):  
Objective Function ◽  
Convex Relaxation ◽  
Large Family ◽  
Quadratic Program ◽  
Feasible Region ◽  
Recession Cone ◽  
Convex Relaxations ◽  
Quadratic Programs ◽  
Alternative Perspective ◽  
Optimal Value

AbstractWe study convex relaxations of nonconvex quadratic programs. We identify a family of so-called feasibility preserving convex relaxations, which includes the well-known copositive and doubly nonnegative relaxations, with the property that the convex relaxation is feasible if and only if the nonconvex quadratic program is feasible. We observe that each convex relaxation in this family implicitly induces a convex underestimator of the objective function on the feasible region of the quadratic program. This alternative perspective on convex relaxations enables us to establish several useful properties of the corresponding convex underestimators. In particular, if the recession cone of the feasible region of the quadratic program does not contain any directions of negative curvature, we show that the convex underestimator arising from the copositive relaxation is precisely the convex envelope of the objective function of the quadratic program, strengthening Burer’s well-known result on the exactness of the copositive relaxation in the case of nonconvex quadratic programs. We also present an algorithmic recipe for constructing instances of quadratic programs with a finite optimal value but an unbounded relaxation for a rather large family of convex relaxations including the doubly nonnegative relaxation.

Nonlinear Optimal Design of Dynamic Mechanical Systems

1992 ◽  
Author(s):  
T. E. Potter ◽  
K. D. Willmert ◽  
M. Sathyamoorthy
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Iteration Process ◽  
Optimization Method ◽  
Linear Constraints ◽  
Sum Of Squares ◽  
Function Evaluation ◽  
Deformation Analysis ◽  
Nonlinear Constraints ◽  
Quadratic Constraints

Abstract Mechanism path generation problems which use link deformations to improve the design lead to optimization problems involving a nonlinear sum-of-squares objective function subjected to a set of linear and nonlinear constraints. Inclusion of the deformation analysis causes the objective function evaluation to be computationally expensive. An optimization method is presented which requires relatively few objective function evaluations. The algorithm, based on the Gauss method for unconstrained problems, is developed as an extension of the Gauss constrained technique for linear constraints and revises the Gauss nonlinearly constrained method for quadratic constraints. The derivation of the algorithm, using a Lagrange multiplier approach, is based on the Kuhn-Tucker conditions so that when the iteration process terminates, these conditions are automatically satisfied. Although the technique was developed for mechanism problems, it is applicable to any optimization problem having the form of a sum of squares objective function subjected to nonlinear constraints.

Prediction of Performance and Design via Optimization of Ducted Propellers Subject to Non-axisymmetric Inflows

2005 ◽  
Author(s):  
Spyros A. Kinnas ◽  
Hanseong Lee ◽  
Hua Gu ◽  
Yumin Deng
Keyword(s):  
Nonlinear Optimization ◽  
Pressure Coefficient ◽  
Optimization Method ◽  
Least Square ◽  
Maximum Efficiency ◽  
Design Parameters ◽  
Blade Design ◽  
Constrained Nonlinear Optimization ◽  
Nonlinear Optimization Method ◽  
Ducted Propellers

Recently developed methods at UT Austin for the analysis of open or ducted propellers are presented, and then coupled with a constrained nonlinear optimization method to design blades of open or ducted propellers for maximum efficiency satisfying the minimum pressure constraint for fully wetted case, or the specified maximum allowable cavity area for cavitating case. A vortex lattice method (named MPUF3A) is applied to analyze the unsteady cavitating performance of open or ducted propellers subject to non-axisymmetric inflows. A finite volume method based Euler solver (named GBFLOW) is applied to predict the flow field around the open or ducted propellers, coupled with MPUF-3A in order to determine the interaction of the propeller with the inflow (i.e. the effective wake) or with the duct. The blade design of open or ducted propeller is performed by using a constrained nonlinear optimization method (named CAVOPT-BASE), which uses a database of computed performance for a set of blade geometries constructed from a base-propeller. The performance is evaluated using MPUF-3A and GBFLOW. CAVOPT-BASE approximates the database using the least square method or the linear interpolation method, and generates the coefficients of polynomials based on the design parameters, such as pitch, chord, and camber. CAVOPT-BASE finally determines the optimum blade design parameters, so that the propeller produces the desired thrust for the given constraints on the pressure coefficient or the allowed amount of cavitation.

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

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