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Probabilistic programming languages represent complex data with intermingled models in a few lines of code. Efficient inference algorithms in probabilistic programming languages make possible to build unified frameworks to compute…
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
Probabilistic inference procedures are usually coded painstakingly from scratch, for each target model and each inference algorithm. We reduce this effort by generating inference procedures from models automatically. We make this code…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
This paper deals with the problem of increasing the minimum distance of a linear code by adding one or more columns to the generator matrix. Several methods to compute extensions of linear codes are presented. Many codes improving the…
While linear programming (LP) decoding provides more flexibility for finite-length performance analysis than iterative message-passing (IMP) decoding, it is computationally more complex to implement in its original form, due to both the…
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the…
We provide a simplified form of Primal Augmented Lagrange Multiplier algorithm. We intend to fill the gap in the steps involved in the mathematical derivations of the algorithm so that an insight into the algorithm is made. The experiment…
They run our lives, if you believe the hype in the news, but there is no precise definition of "algorithms" which is generally accepted by the mathematicians, logicians and computer scientists who create and study them. My main aims here…
In this paper we develop a very special substitution method for solving a general linear programming problem (LPP). Of course the substitution is a kind of elimination of variable but this method must not be confused with the so-called…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…
This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to solve…
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
Interpolation-based techniques have been widely and successfully applied in the verification of hardware and software, e.g., in bounded-model check- ing, CEGAR, SMT, etc., whose hardest part is how to synthesize interpolants. Various work…
We reconsider the ellipsoid method for linear inequalities. Using the ellipsoid representation of Burrell and Todd, we show the method can be viewed as coordinate descent on the volume of an enclosing ellipsoid, or on a potential function,…
This paper provides a set of cycling problems in linear programming. These problems should be useful for researchers to develop and test new simplex algorithms. As matter of the fact, this set of problems is used to test a recently proposed…