1,865 research outputs found
A sequential semidefinite programming method and an application in passive reduced-order modeling
We consider the solution of nonlinear programs with nonlinear
semidefiniteness constraints. The need for an efficient exploitation of the
cone of positive semidefinite matrices makes the solution of such nonlinear
semidefinite programs more complicated than the solution of standard nonlinear
programs. In particular, a suitable symmetrization procedure needs to be chosen
for the linearization of the complementarity condition. The choice of the
symmetrization procedure can be shifted in a very natural way to certain linear
semidefinite subproblems, and can thus be reduced to a well-studied problem.
The resulting sequential semidefinite programming (SSP) method is a
generalization of the well-known SQP method for standard nonlinear programs. We
present a sensitivity result for nonlinear semidefinite programs, and then
based on this result, we give a self-contained proof of local quadratic
convergence of the SSP method. We also describe a class of nonlinear
semidefinite programs that arise in passive reduced-order modeling, and we
report results of some numerical experiments with the SSP method applied to
problems in that class
A recursively feasible and convergent Sequential Convex Programming procedure to solve non-convex problems with linear equality constraints
A computationally efficient method to solve non-convex programming problems
with linear equality constraints is presented. The proposed method is based on
a recursively feasible and descending sequential convex programming procedure
proven to converge to a locally optimal solution. Assuming that the first
convex problem in the sequence is feasible, these properties are obtained by
convexifying the non-convex cost and inequality constraints with inner-convex
approximations. Additionally, a computationally efficient method is introduced
to obtain inner-convex approximations based on Taylor series expansions. These
Taylor-based inner-convex approximations provide the overall algorithm with a
quadratic rate of convergence. The proposed method is capable of solving
problems of practical interest in real-time. This is illustrated with a
numerical simulation of an aerial vehicle trajectory optimization problem on
commercial-of-the-shelf embedded computers
An interior-point method for the single-facility location problem with mixed norms using a conic formulation
We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in R, where each distance can be measured according to a different p-norm.We show how this problem can be expressed into a structured conic format by decomposing the nonlinear components of the objective into a series of constraints involving three-dimensional cones. Using the availability of a self-concordant barrier for these cones, we present a polynomial-time algorithm (a long-step path-following interior-point scheme) to solve the problem up to a given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem.nonsymmetric conic optimization, conic reformulation, convex optimization, sum of norm minimization, single-facility location problems, interior-point methods
- …