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.

Efficient mixed-integer planning for UAVs in cluttered environments

Abstract: We present a new approach to the design of smooth trajectories for quadrotor unmanned aerial vehicles (UAVs), which are free of collisions with obstacles along their entire length. To avoid the non-convex constraints normally required for obstacle-avoidance, we perform a mixed-integer optimization in which polynomial trajectories are assigned to convex regions which are known to be obstacle-free. Prior approaches have used the faces of the obstacles themselves to define these convex regions. We instead use IRIS, a recently developed technique for greedy convex segmentation [1], to pre-compute convex regions of safe space. This results in a substantially reduced number of integer variables, which improves the speed with which the optimization can be solved to its global optimum, even for tens or hundreds of obstacle faces. In addition, prior approaches have typically enforced obstacle avoidance at a finite set of sample or knot points. We introduce a technique based on sums-of-squares (SOS) programming that allows us to ensure that the entire piecewise polynomial trajectory is free of collisions using convex constraints. We demonstrate this technique in 2D and in 3D using a dynamical model in the Drake toolbox for Matlab [2].

Fortran package for nonlinear programming. User's Guide for NPSOL (Version 4. 0)

Abstract: This report forms the user's guide for Version 4.0 of NPSOL, a set of Fortran subroutines designed to minimize a smooth function subject to constraints, which may include simple bounds on the variables, linear constraints and smooth nonlinear constraints. (NPSOL may also be used for unconstrained, bound-constrained and linearly constrained optimization.). The user must provide subroutines that define the objective and constraint functions and (optionally) their gradients. All matrices are treated as dense, and hence NPSOL is not intended for large sparse problems. NPSOL uses a sequential quadratic programming (SQP) algorithm, in which the search direction is the solution of a quadratic programming (QP) subproblem. The algorithm treats bounds, linear constraints and nonlinear constraints separately. The Hessian of each QP subproblem is a positive-definite quasi-Newton approximation to the Hessian of the Lagrangian function. The steplength at each iteration is required to produce a sufficient decrease in an augmented Lagrangian merit function. Each QP subproblem is solved using a quadratic programming package with several features that improve the efficiency of an SQP algorithm.

Exact penalty functions in nonlinear programming

Abstract: In this paper some new theoretic results on piecewise differentiable exact penalty functions are presented. Sufficient conditions are given for the existence of exact penalty functions for inequality constrained problems more general than concave and several classes of such functions are presented.

Multiuser Optimization: Distributed Algorithms and Error Analysis

Abstract: Traditionally, a multiuser problem is a constrained optimization problem characterized by a set of users, an objective given by a sum of user-specific utility functions, and a collection of linear constraints that couple the user decisions. The users do not share the information about their utilities, but do communicate values of their decision variables. The multiuser problem is to maximize the sum of the user-specific utility functions subject to the coupling constraints, while abiding by the informational requirements of each user. In this paper, we focus on generalizations of convex multiuser optimization problems where the objective and constraints are not separable by user and instead consider instances where user decisions are coupled, both in the objective and through nonlinear coupling constraints. To solve this problem, we consider the application of gradient-based distributed algorithms on an approximation of the multiuser problem. Such an approximation is obtained through a Tikhonov regulariza...

Unit commitment by tabu search

Abstract: An application of the tabu search (TS) method to solve the unit commitment problem (UCP) is presented. The TS seeks to counter the danger of entrapment at a local optimum by incorporating a memory structure that forbids or penalises certain moves that would return to recently visited solutions. New rules for randomly generating feasible solutions for the UCP are introduced. The problem is divided into two subproblems: a combinatorial optimisation problem and a nonlinear programming problem. The former is solved using the tabu search algorithm (TSA) while the latter problem is solved via a quadratic programming routine. Numerical results show an improvement in the solution cost compared to previously obtained results.