Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

A combined optimization method for solving the inverse kinematics problems of mechanical manipulators

Abstract: A new method for computing numerical solutions to the inverse kinematics problem of robotic manipulators is developed. The method is based on a combination of two nonlinear programming techniques and the forward recursion formulas, with the joint limitations of the robot being handled implicitly as simple boundary constraints. This method is numerically stable since it converges to the correct answer with virtually any initial approximation, and it is not sensitive to the singular configuration of the manipulator. In addition, this method is computationally efficient and can be applied to serial manipulators having any number of degrees of freedom. >

Nonlinear control of constrained linear systems via predictive reference management

Abstract: A method based on conceptual tools of predictive control is described for solving set-point tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device, called command governor (CG), whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time a virtual sequence among a family of linearly parameterized command sequences, by solving a convex constrained quadratic optimization problem, and feeds the primal system according to a receding horizon control philosophy. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behavior, provided that an admissibility condition on the initial state is satisfied. Though the CG can be tailored for the application at hand by appropriately choosing the available design knobs, the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem.

Physical programming - Effective optimization for computational design

Abstract: A new effective and computationally efficient approach for design optimization, hereby entitled physical programming, is developed. This new approach is intended to substantially reduce the computational intensity of large problems and to place the design process into a more flexible and natural framework. Knowledge of the desired attributes of the optimal design is judiciously exploited. For each attribute of interest to the designer (each criterion), regions are defined that delineate degrees of desirability : unacceptable, highly undesirable, undesirable, tolerable, desirable, and highly desirable. This approach completely eliminates the need for iterative weight setting, which is the object of the typical computational bottleneck in large design optimization problems. Two key advantages of physical programming are 1) once the designer's preferences are articulated, obtaining the corresponding optimal design is a noniterative process-in stark contrast to conventional weight-based methods and 2) it provides the means to reliably employ optimization with minimal prior knowledge thereof. The mathematical infrastructure that supports the physical programming design optimization framework is developed, and a numerical example provided. Physical programming is a new approach to realistic design optimization that may be appealing to the design engineer in an industrial setting.