Brian Borchers

CSDP, A C library for semidefinite programming

This paper describes CSDP, a library of routines that implements a predictor corrector variant of the semidefinite programming algorithm of Helmberg, Rendl, Vanderbei, and Wolkowicz. The main advantages of this code are that it can be used as a stand alone solver or as a callable subroutine, that it is written in C for efficiency, that it makes effective use of sparsity in the constraint matrices, and that it includes support for linear inequality constraints in addition to linear equality constraints. We discuss the algorithm used, its computational complexity, and storage requirements. Finally, we present benchmark results for a collection of test problems.

An improved branch and bound algorithm for mixed integer nonlinear programs

Abstract This paper describes an improved branch and bound code for zero-one mixed integer nonlinear programs with convex objective functions and constraints. The code uses Lagrangian duality to obtain lower bounds. The code also uses early branching to avoid solving some subproblems to optimality. Computational results show substantial performance improvements on many problems.

A Two-Phase Exact Algorithm for MAX-SAT and Weighted MAX-SAT Problems

We describe a two-phase algorithm for MAX-SAT and weighted MAX-SAT problems. In the first phase, we use the GSAT heuristic to find a good solution to the problem. In the second phase, we use an enumeration procedure based on the Davis-Putnam-Loveland algorithm, to find a provably optimal solution. The first heuristic stage improves the performance of the algorithm by obtaining an upper bound on the minimum number of unsatisfied clauses that can be used in pruning branches of the search tree.We compare our algorithm with an integer programming branch-and-cut algorithm. Our implementation of the two-phase algorithm is faster than the integer programming approach on many problems. However, the integer programming approach is more effective than the two-phase algorithm on some classes of problems, including MAX-2-SAT problems.

An Automatic, Adaptive Algorithm for Refining Phase Picks in Large Seismic Data Sets

We have developed an adaptive, automatic, correlation- and clustering- based method for greatly reducing the degree of picking inconsistency in large, digital seismic catalogs and for quantifying similarity within, and discriminating among, clusters of disparate waveform families. Innovations in the technique include (1) the use of eigenspectral methods for cross-spectral phase estimation and for providing subsample pick lag error estimates in units of time, as opposed to dimensionless relative scaling of uncertainties; (2) adaptive, cross-coherency-based filtering; and (3) a hierarchical waveform stack correlation method for adjusting mean intercluster pick times without compromising tight intracluster relative pick estimates. To solve the systems of cross-correlation lags we apply an iterative, optimized conjugate gra- dient technique that minimizes an L1-norm misfit. Our repicking technique not only provides robust similarity classification-event discrimination without making a priori assumptions regarding waveform similarity as a function of preliminary hypocenter estimates, but also facilitates high-resolution relocation of seismic sources. Although knowledgeable user input is needed initially to establish run-time parameters, sig- nificant improvement in pick consistency and waveform-based event classification may be obtained by then allowing the programs to operate automatically on the data. The process shows promise for enhancing catalog reliability while at the same time reducing analyst workload, although careful assessment of the automatic results is still important.

SDPLIB 1.2, a library of semidefinite programming test problems

SDPLIB is a collection of semidefinite programming (SDP) test problems. The problems are drawn from a variety of applications, including truss topology design, control systems engineering, and relaxations of combinatorial optimization problems. The current version of the library contains a total of 92 SDP problems encoded in a standard format. It is hoped that SDPLIB will stimulate the development of improved software for the solution of SDP problems.

Using Automated, High-precision Repicking to Improve Delineation of Microseismic Structures at the Soultz Geothermal Reservoir

Abstract — An automatic, adaptive, correlation-based algorithm for adjusting phase picks in large digital seismic data sets provides significant improvement in resolution of microseismic structures using only a small fraction of the time and manpower which would be required to re-analyze waveforms manually or semi-automatically. We apply this technique to induced seismicity at the Soultz-sous-Forêts geothermal site, France. The method is first applied to a small, previously manually repicked subset of the catalogue so that we may compare our results to those obtained from painstaking, visual, cross-correlation-based techniques. Relative centroid-adjusted hypocenters show a decrease in median mislocation from 31 to 7 m for preliminary and automatically adjusted picks, respectively, compared to the manual results. Narrow, intersecting joint features not observed in the preliminary hypocenter cloud, but revealed through manual repicking, are also recovered using the automatic method. We then address a larger catalogue of ∼7000 microearthquakes. After relocating the events using automatic repicks, the percentage of events clustering within 5 m of their nearest neighbor increases form 5 to 26% of the catalogue. Hypocenter relocations delineate narrow, linear features previously obscured within the seismic cloud, interpreted as faults or fractures which may correspond to fluid propagation paths, or to changes in stress as a result of elevated pore pressures. RMS travel-time residuals for the larger data set are reduced by only 0.2%; however, phase-pick biases in the preliminary catalogue have influenced both the velocity model and station correction calculations, which will affect location residuals. These pick biases are apparent on the adjusted, stacked waveforms and correcting them will be important prior to future velocity model refinements.

Solving Linear Ordering Problems with a Combined Interior Point/Simplex Cutting Plane Algorithm

We describe a cutting plane algorithm for solving linear ordering problems. The algorithm uses a primal-dual interior point method to solve the first few relaxations and then switches to a simplex method to solve the last few relaxations. The simplex method uses CPLEX 4.0. We compare the algorithm with one that uses only an interior point method and with one that uses only a simplex method. We solve integer programming problems with as many as 31125 binary variables. Computational results show that the combined approach can dramatically outperform the other two methods.

Comparison of inverse methods for reconstructing the release history of a groundwater contamination source.

Inverse methods can be used to reconstruct the release history of a known source of groundwater contamination from concentration data describing the present-day spatial distribution of the contaminant plume. Using hypothetical release history functions and contaminant plumes, we evaluate the relative effectiveness of two proposed inverse methods, Tikhonov regularization (TR) and minimum relative entropy (MRE) inversion, in reconstructing the release history of a conservative contaminant in a one-dimensional domain [Skaggs and Kabala, 1994; Woodbury and Ulrych, 1996]. We also address issues of reproducibility of the solution and the appropriateness of models for simulating random measurement error. The results show that if error-free plume concentration data are available, both methods perform well in reconstructing a smooth source history function. With error-free data the MRE method is more robust than TR in reconstructing a nonsmooth source history function; however, the TR method is more robust if the data contain measurement error. Two error models were evaluated in this study, and we found that the particular error model does not affect the reliability of the solutions. The results for the TR method have somewhat greater reproducibility because, in some cases, its input parameters are less subjective than those of the MRE method; however, the MRE solution can identify regions where the data give little or no information about the source history function, while the TR solution cannot.

Methods for prediction of soil dielectric properties: a review

Electromagnetic sensors such as ground penetrating radar and electromagnetic induction sensors are among the most widely used methods for the detection of buried land mines and unexploded ordnance. However, the performance of these sensors depends on the dielectric properties of the soil, which in turn are related to soil properties such as texture, bulk density, and water content. To predict the performance of electromagnetic sensors it is common to estimate the soil dielectric properties using models. However, the wide variety of available models, each with its own characteristics, makes it difficult to select the appropriate one for each occasion. In this paper we present an overview of the available methods, ranging from phenomenological Cole-Cole and Debye models to volume-based dielectric mixing models, and (semi-) empirical pedotransfer functions.

Solving Real-World Linear Ordering Problems Using a Primal-Dual Interior Point Cutting Plane Method

Cutting plane methods require the solution of a sequence of linear programs, where the solution to one provides a warm start to the next. A cutting plane algorithm for solving the linear ordering problem is described. This algorithm uses the primaldual interior point method to solve the linear programming relaxations. A point which is a good warm start for a simplex-based cutting plane algorithm is generally not a good starting point for an interior point method. Techniques used to improve the warm start include attempting to identify cutting planes early and storing an old feasible point, which is used to help recenter when cutting planes are added. Computational results are described for some real-world problems; the algorithm appears to be competitive with a simplex-based cutting plane algorithm.