The object-oriented software package OOQP for solving convex quadratic programming problems (QP) is described. The primal-dual interior point algorithms supplied by OOQP are implemented in a way that is largely independent of the problem structure. Users may exploit problem structure by supplying linear algebra, problem data, and variable classes that are customized to their particular applications. The OOQP distribution contains default implementations that solve several important QP problem types, including general sparse and dense QPs, bound-constrained QPs, and QPs arising from support vector machines and Huber regression. The implementations supplied with the OOQP distribution are based on such well known linear algebra packages as MA27/57, LAPACK, and PETSc. OOQP demonstrates the usefulness of object-oriented design in optimization software development, and establishes standards that can be followed in the design of software packages for other classes of optimization problems. A number of the classes in OOQP may also be reusable directly in other codes.

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The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of L does not change, it is not suitable for methods that modify a sparse Cholesky factorization after a low-rank change to A (an update/downdate, A = A±WW T). Supernodes merge and split apart during an update/downdate. Dynamic supernodes are introduced, which allow a sparse Cholesky update/downdate to obtain performance competitive with conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional (BLAS-based) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse Cholesky factorization and update/downdate package, which forms the basis of x=A\b in MAT-LAB when A is sparse and symmetric positive definite. 1

CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLAB TM interfaces. It appears in MATLAB 7.2 as x=A\b when A is sparse symmetric positive definite, as well as in several other sparse matrix functions. 1

Indexed data structures are prevalent in many programming applications. Collection-oriented languages provide means to operate directly on these structures, rather than having to loop or recurse through them. This style of programming will often yield clear and succinct programs. However, these programming languages will often provide only a limited choice of indexed data types and primitives, and the exact semantics of these primitives will sometimes vary with the data type and language. In this paper we develop a unifying semantical model for indexed data structures. The purpose is to support the construction of abstract data types and language features for such structures from first principles, such that they are largely generic over many kinds of data structures. The use of these abstract data types can make programs and their semantics less dependent of the actual data structure. This makes programs more portable across different architectures and facilitates the early design phase. The model is a generalisation of arrays, which we call data fields: these are functions with explicit information about their domains. This information can be conventional array bounds but it could also define other shapes, for instance sparse. Data fields can be interpreted as partial functions, and we define a metalanguage for partial functions. In this language we define abstract versions of collection-oriented operations, and we show a number of identities for them. This theory is used to guide the design of data fields and their operations so they correspond closely to the more abstract notion of partial functions. We define phi-abstraction, a lambda-like syntax for defining data fields in a shape-independent manner, and prove a theorem which relates phi-abstraction and lambda-abstraction semantically. We also define a small data field language whose semantics is given by formal data fields, and give examples of data field programming for parallel algorithms with arrays and sparse structures, database quering and computing, and specification of symbolic drawings.

this paper we briefly review different approaches to constructing the ABCs available in the literature. Then, we describe the results associated with the use of one particular technique - the difference potentials (DPM) method by Ryaben'kii. The ABCs obtained by means of the DPM allow one to simultaneously meet the high accuracy standards and the requirements of geometric universality and easiness in implementation. In other words, this technique combines the advantages relevant to different classes of previously developed methods. The DPM-based ABCs have recently led to major improvements in performance and robustness of flow computations.

. We present Oblio, a sparse direct solver library running in both serial an parallel environments. The code is written in C++ using object-oriented techniques, with the exception of few computationally intensive kernels that are written in Fortran 77. In this paper we explain what motivated the project, discuss design issues and report recent results. 1 Introduction As shown in [1], computing the solution of sparse linear systems of equations represents the key computation in several critical industry and national-security applications. Among the problems identified are the optimization of aircraft turbines, the design of public-key cryptosystems, and a broad range of other applications in computational fluid dynamics, linear programming, finite-element methods and process engineering. We currently investigate sparse direct solvers, which are more robust than their iterative counterparts. The drawback is that they require more computational resources and they are more difficult...

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