Abstract. Markov and Conditional random fields (CRFs) used in computer vision typically model only local interactions between variables, as this is computationally tractable. In this paper we consider a class of global potentials defined over all variables in the CRF. We show how they can be readily optimised using standard graph cut algorithms at little extra expense compared to a standard pairwise field. This result can be directly used for the problem of class based image segmentation which has seen increasing recent interest within computer vision. Here the aim is to assign a label to each pixel of a given image from a set of possible object classes. Typically these methods use random fields to model local interactions between pixels or super-pixels. One of the cues that helps recognition is global object co-occurrence statistics, a measure of which classes (such as chair or motorbike) are likely to occur in the same image together. There have been several approaches proposed to exploit this property, but all of them suffer from different limitations and typically carry a high computational cost, preventing their application on large images. We find that the new model we propose produces an improvement in the labelling compared to just using a pairwise model. 1

One of the main drawbacks associated with Interior Point Methods (IPM) is the perceived lack of an efficient warmstarting scheme which would enable the use of information from a previous solution of a similar problem. Recently there has been renewed interest in the subject. A common problem with warmstarting for IPM is that an advanced starting point which is close to the boundary of the feasible region, as is typical, might lead to blocking of the search direction. Several techniques have been proposed to address this issue. Most of these aim to lead the iterate back into the interior of the feasible region- we classify them as either “modification steps ” or “unblocking steps ” depending on whether the modification is taking place before solving the modified problem to prevent future problems, or during the solution if and when problems become apparent. A new “unblocking ” strategy is suggested which attempts to directly address the issue of blocking by performing sensitivity analysis on the Newton step with the aim of increasing the size of the step that can be taken. This analysis is used in a new technique to warmstart

Constraint-reduction schemes have been proposed for the solution by interior-point methods of linear programs with many more inequality constraints than variables in standard dual form. Such schemes have been shown to be provably convergent and highly efficient in practice. A critical requirement of these schemes is the availability of an initial dual-feasible point. In this paper, building on a general framework (which encompasses several previously proposed approaches) for dual-feasible constraint-reduced interior-point optimization, for which we prove convergence to a single point of the sequence of dual iterates, we propose a framework for “infeasible ” constraint-reduced interior-point optimization. Central to this framework is an exact (ℓ1 or ℓ∞) penalty function scheme endowed with a mechanism for iterative adjustment of the penalty parameter, which aims at yielding, after a finite number of iterations, a value that guarantees feasibility (for the original problem) of the minimizers. Finiteness of the sequence of penalty parameter adjustments is proved under mild assumptions for all algorithms that fit within the framework, including “infeasible ” extensions of a “dual ” algorithm proposed in the early 1990s and of two recently proposed “primal-dual ” algorithms. One of the latter two, a constraint-reduced variant of Mehrotra’s Predictor-Corrector algorithm, is then more specifically considered: further convergence results are proved, and numerical results are reported that demonstrate that the approach is of practical interest.

Abstract not found

multi-step interior point warm-start approach for

Second-order cone programming with warm start for

extent that it included research on robust algorithms in sensor network localization. While there is some overlap with the research in this proposal, the NSERC research focuses on developing robust algorithms for this problem, while the MITACS-funded research is concerned with developing algorithms for large-scale problems. Hence the two grants are supporting different facets of research on the same problem. Steve Vavasis receives funding from NSERC and (jointly with Henry Wolkowicz and Thomas Coleman) from CFI. NSERC funds his research in preconditioning and matrix approximation. The NSERC project is aimed at different applications, such as the solution of differ-A. Vannelli and M.F. Anjos- HPO and Applications: Titles and Investigators 2 ential equations. The CFI funds are specifically for a cluster computer for computational optimization. Miguel Anjos receives funding from NSERC and (jointly with Kankar Bhattacharya) from CFI. NSERC funds his fundamental research on semidefinite programmings models for hard combinatorial problems arising in engineering applications. This is separate from the research supported by MITACS: the vast majority of funding from MITACS has been supporting student on research projects in the areas of power engineering and ambulance dispatch and deployment; these projects are co-funded by industry or other non-academic partners,

Quadratic programming (QP) problems arise naturally in a variety of applications. In many cases, a good estimate of the solution may be available. It is desirable to be able to utilize such information in order to reduce the computational cost of finding the solution. Activeset methods for solving QP problems differ from interior-point methods in being able to take full advantage of such warm-start situations. QPBLU is a new Fortran 95 package for minimizing a convex quadratic function with linear constraints and bounds. QPBLU is an active-set method that uses block-LU updates of an initial KKT system to handle active-set changes as well as low-rank Hessian updates. It is intended for convex QP problems in which the linear constraint matrix is sparse and many degrees of freedom are expected at the solution. Warm start capabilities allow the solver to take advantage of good estimates of the optimal active set or solution. A key feature of the method is the ability to utilize a variety of sparse linear system packages to solve the KKT systems. QPBLU has been tested on QP problems derived from linear programming problems

This research studies two computational techniques that improve the practical performance of existing implementations of interior point methods for linear programming. Both are based on the concept of symmetric neighbourhood as the driving tool for the analysis of the good performance of some practical algorithms. The symmetric neighbourhood adds explicit upper bounds on the complementarity