150,452 research outputs found
Mathematical Programming Decoding of Binary Linear Codes: Theory and Algorithms
Mathematical programming is a branch of applied mathematics and has recently
been used to derive new decoding approaches, challenging established but often
heuristic algorithms based on iterative message passing. Concepts from
mathematical programming used in the context of decoding include linear,
integer, and nonlinear programming, network flows, notions of duality as well
as matroid and polyhedral theory. This survey article reviews and categorizes
decoding methods based on mathematical programming approaches for binary linear
codes over binary-input memoryless symmetric channels.Comment: 17 pages, submitted to the IEEE Transactions on Information Theory.
Published July 201
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Reformulations of mathematical programming problems as linear complementarity problems
A family of complementarity problems are defined as extensions of the well known Linear Complementarity Problem (LCP). These are
(i.) Second Linear Complementarity Problem (SLCP) which is an LCP extended by introducing further equality restrictions and unrestricted variables,
(ii.) Minimum Linear Complementarity Problem (MLCP) which is an
LCP with additional variables not required to be complementary and with a linear objective function which is to be minimized,
(iii.) Second Minimum Linear Complementarity Problem (SMLCP) which is an MLCP but the nonnegative restriction on one of each pair of complementary variables is relaxed so that it is allowed to be unrestricted in value.
A number of well known mathematical programming problems, namely quadratic programming (convex, nonconvex, pseudoconvex nonconvex), bilinear programming, game theory, zero-one integer programming, the fixed charge problem, absolute value programming, variable separable programming are reformulated as members of this family of four complementarity problems
On Relation between Constraint Answer Set Programming and Satisfiability Modulo Theories
Constraint answer set programming is a promising research direction that
integrates answer set programming with constraint processing. It is often
informally related to the field of satisfiability modulo theories. Yet, the
exact formal link is obscured as the terminology and concepts used in these two
research areas differ. In this paper, we connect these two research areas by
uncovering the precise formal relation between them. We believe that this work
will booster the cross-fertilization of the theoretical foundations and the
existing solving methods in both areas. As a step in this direction we provide
a translation from constraint answer set programs with integer linear
constraints to satisfiability modulo linear integer arithmetic that paves the
way to utilizing modern satisfiability modulo theories solvers for computing
answer sets of constraint answer set programs.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
A Computational Comparison of Optimization Methods for the Golomb Ruler Problem
The Golomb ruler problem is defined as follows: Given a positive integer n,
locate n marks on a ruler such that the distance between any two distinct pair
of marks are different from each other and the total length of the ruler is
minimized. The Golomb ruler problem has applications in information theory,
astronomy and communications, and it can be seen as a challenge for
combinatorial optimization algorithms. Although constructing high quality
rulers is well-studied, proving optimality is a far more challenging task. In
this paper, we provide a computational comparison of different optimization
paradigms, each using a different model (linear integer, constraint programming
and quadratic integer) to certify that a given Golomb ruler is optimal. We
propose several enhancements to improve the computational performance of each
method by exploring bound tightening, valid inequalities, cutting planes and
branching strategies. We conclude that a certain quadratic integer programming
model solved through a Benders decomposition and strengthened by two types of
valid inequalities performs the best in terms of solution time for small-sized
Golomb ruler problem instances. On the other hand, a constraint programming
model improved by range reduction and a particular branching strategy could
have more potential to solve larger size instances due to its promising
parallelization features
A Comparison of Mixed-Integer Programming Models for Non-Convex Piecewise Linear Cost Minimization Problems
We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory
Engineering Optimization: Methods/Applications - Colorado State University
This course provides a comprehensive treatment of methods of optimization with focus on linear programming and its extensions, network flow optimization, integer programming, quadratic programming, and an introduction to nonlinear programming. The goal is to maintain a balance between theory, numerical computation, problem setup for solution by computer algorithms, and engineering applications. Course taught at Colorado State University
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