This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be … Read more
APPSPACK is software for solving unconstrained and bound constrained optimization problems. It implements an asynchronous parallel pattern search method that has been specifically designed for problems characterized by expensive function evaluations. Using APPSPACK to solve optimization problems has several advantages: No derivative information is needed; the procedure for evaluating the objective function can be executed … Read more
Pattern search methods can be made more efficient if past function evaluations are appropriately reused. In this paper we will introduce a number of ways of reusing previous evaluations of the objective function based on the computation of simplex derivatives (e.g., simplex gradients) to improve the efficiency of a pattern search iteration. At each iteration … Read more
In this paper, we formulate a nonlinear, nonconvex semidefinite optimization problem to select the steady-state free precession (SSFP) pulse-sequence design variables which maximize the contrast to noise ratio in tissue segmentation. The method could be applied to other pulse sequence types, arbitrary numbers of tissues, and numbers of images. To solve the problem we use … Read more
In this paper we present an interior point method for large scale Signorini elastic contact problems. We study the case of an elastic body in frictionless contact with a rigid foundation. Primal and primal-dual algorithms are developed to solve the quadratic optimization problem arising in the variational formulation. Our computational study confirms the efficiency of … Read more
The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algorithmic parameters. This is done by devising a general framework for parameter tuning. The framework makes provision for surrogate objectives. Parameters are sought so as to minimize some measure of performance of … Read more
We consider optimization problems with inequality and abstract set constraints, and we derive sensitivity properties of Lagrange multipliers under very weak conditions. In particular, we do not assume uniqueness of a Lagrange multiplier or continuity of the perturbation function. We show that the Lagrange multiplier of minimum norm defines the optimal rate of improvement of … Read more
Bundle adjustment using the Levenberg-Marquardt minimization algorithm is almost invariably used as the last step of every feature-based structure and motion estimation computer vision algorithm to obtain optimal 3D structure and viewing parameter estimates. However, due to the large number of unknowns contributing to the minimized reprojection error, a general purpose implementation of the Levenberg-Marquardt … Read more
Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of supports for sums of squares (SOS) polynomials that lead to efficient SOS and semidefinite programming (SDP) … Read more
We study a sequential algorithm for finding the projection of a given point onto the common fixed points set of a semigroup of nonexpansive operators in Hilbert space. The convergence of such an algorithm was previously established only for finitely many nonexpansive operators. Algorithms of this kind have been applied to the best approximation and … Read more