16,749 research outputs found
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 second derivative SQP method: theoretical issues
Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a second-derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which “guides” the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established
Efficient algorithm for solving semi-infinite programming problems and their applications to nonuniform filter bank designs
An efficient algorithm for solving semi-infinite programming problems is proposed in this paper. The index set is constructed by adding only one of the most violated points in a refined set of grid points. By applying this algorithm for solving the optimum nonuniform symmetric/antisymmetric linear phase finite-impulse-response (FIR) filter bank design problems, the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorith
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 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
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