45 research outputs found
Optimizing Memory-Bounded Controllers for Decentralized POMDPs
We present a memory-bounded optimization approach for solving
infinite-horizon decentralized POMDPs. Policies for each agent are represented
by stochastic finite state controllers. We formulate the problem of optimizing
these policies as a nonlinear program, leveraging powerful existing nonlinear
optimization techniques for solving the problem. While existing solvers only
guarantee locally optimal solutions, we show that our formulation produces
higher quality controllers than the state-of-the-art approach. We also
incorporate a shared source of randomness in the form of a correlation device
to further increase solution quality with only a limited increase in space and
time. Our experimental results show that nonlinear optimization can be used to
provide high quality, concise solutions to decentralized decision problems
under uncertainty.Comment: Appears in Proceedings of the Twenty-Third Conference on Uncertainty
in Artificial Intelligence (UAI2007
Solving mathematical programs with complementarity constraints with nonlinear solvers
MPCC can be solved with specific MPCC codes or in its nonlinear
equivalent formulation (NLP) using NLP solvers. Two NLP solvers - NPSOL and
the line search filter SQP - are used to solve a collection of test problems in AMPL.
Both are based on SQP (Sequential Quadratic Programming) philosophy but the
second one uses a line search filter scheme.(undefined
A line search filter approach for the system of nonlinear equations
AbstractSome constrained optimization approaches have been recently proposed for the system of nonlinear equations (SNE). Filter approach with line search technique is employed to attack the system of nonlinear equations in this paper. The system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved by line search strategy. Furthermore, at each step, some equations are treated as constraints while the others act as objective functions, and filter strategy is then utilized. In essence, constrained optimization methods combined with filter technique are utilized to cope with the system of nonlinear equations
Solving Mathematical Programs with Equilibrium Constraints as Nonlinear Programming: A New Framework
We present a new framework for the solution of mathematical programs with
equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is
viewed as a concentration of an unconstrained optimization which minimizes the
complementarity measure and a nonlinear programming with general constraints. A
strategy generalizing ideas of Byrd-Omojokun's trust region method is used to
compute steps. By penalizing the tangential constraints into the objective
function, we circumvent the problem of not satisfying MFCQ. A trust-funnel-like
strategy is used to balance the improvements on feasibility and optimality. We
show that, under MPEC-MFCQ, if the algorithm does not terminate in finite
steps, then at least one accumulation point of the iterates sequence is an
S-stationary point
A Filter Algorithm with Inexact Line Search
A filter algorithm with inexact line search is proposed
for solving nonlinear programming problems. The filter is constructed by employing
the norm of the gradient of the Lagrangian function to the infeasibility
measure. Transition to superlinear local convergence is showed for the proposed
filter algorithm without second-order correction. Under mild conditions, the
global convergence can also be derived. Numerical experiments show the efficiency
of the algorithm
A penalty-function-free line search SQP method for nonlinear programming
AbstractWe propose a penalty-function-free non-monotone line search method for nonlinear optimization problems with equality and inequality constraints. This method yields global convergence without using a penalty function or a filter. Each step is required to satisfy a decrease condition for the constraint violation, as well as that for the objective function under some reasonable conditions. The proposed mechanism for accepting steps also combines the non-monotone technique on the decrease condition for the constraint violation, which leads to flexibility and an acceptance behavior comparable with filter based methods. Furthermore, it is shown that the proposed method can avoid the Maratos effect if the search directions are improved by second-order corrections (SOC). So locally superlinear convergence is achieved. We also present some numerical results which confirm the robustness and efficiency of our approach
Nonlinear programming without a penalty function or a filter
A new method is introduced for solving equality constrained nonlinear optimization problems. This method does not use a penalty function, nor a barrier or a filter, and yet can be proved to be globally convergent to first-order stationary points. It uses different trust-regions to cope with the nonlinearities of the objective function and the constraints, and allows inexact SQP steps that do not lie exactly in the nullspace of the local Jacobian. Preliminary numerical experiments on CUTEr problems indicate that the method performs well
A coupling of discrete and continuous optimization to solve kinodynamic motion planning problems
A new approach to find the fastest trajectory of a robot avoiding obstacles, is presented. This optimal trajectory is the solution of an optimal control problem with kinematic and dynamics constraints. The approach involves a direct method based on the time discretization of the control variable. We mainly focus on the computation of a good initial trajectory. Our method combines discrete and continuous optimization concepts. First, a graph search algorithm is used to determine a list of via points. Then, an optimal control problem of small size is defined to find the fastest trajectory that passes through the vicinity of the via points. The resulting solution is the initial trajectory. Our approach is applied to a single body mobile robot. The numerical results show the quality of the initial trajectory and its low computational cost
A coupling of discrete and continuous optimization to solve kinodynamic motion planning problems
A new approach to find the fastest trajectory of a robot avoiding
obstacles, is presented. This optimal trajectory is the solution of an
optimal control problem with kinematic and dynamics constraints. The approach
involves a direct method based on the time discretization of the control
variable. We mainly focus on the computation of a good initial trajectory.
Our method combines discrete and continuous optimization concepts. First, a
graph search algorithm is used to determine a list of via points. Then, an
optimal control problem of small size is defined to find the fastest
trajectory that passes through the vicinity of the via points. The resulting
solution is the initial trajectory. Our approach is applied to a single body
mobile robot. The numerical results show the quality of the initial
trajectory and its low computational cost