4,936 research outputs found
On Weighted Low-Rank Approximation
Our main interest is the low-rank approximation of a matrix in R^m.n under a
weighted Frobenius norm. This norm associates a weight to each of the (m x n)
matrix entries. We conjecture that the number of approximations is at most
min(m, n).
We also investigate how the approximations depend on the weight-values.Comment: 13 page
A Framework for Globally Optimizing Mixed-Integer Signomial Programs
Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York
Minimal average degree aberration and the state polytope for experimental designs
For a particular experimental design, there is interest in finding which
polynomial models can be identified in the usual regression set up. The
algebraic methods based on Groebner bases provide a systematic way of doing
this. The algebraic method does not in general produce all estimable models but
it can be shown that it yields models which have minimal average degree in a
well-defined sense and in both a weighted and unweighted version. This provides
an alternative measure to that based on "aberration" and moreover is applicable
to any experimental design. A simple algorithm is given and bounds are derived
for the criteria, which may be used to give asymptotic Nyquist-like
estimability rates as model and sample sizes increase
A tractable class of binary VCSPs via M-convex intersection
A binary VCSP is a general framework for the minimization problem of a
function represented as the sum of unary and binary cost functions. An
important line of VCSP research is to investigate what functions can be solved
in polynomial time. Cooper and \v{Z}ivn\'{y} classified the tractability of
binary VCSP instances according to the concept of "triangle," and showed that
the only interesting tractable case is the one induced by the joint winner
property (JWP). Recently, Iwamasa, Murota, and \v{Z}ivn\'{y} made a link
between VCSP and discrete convex analysis, showing that a function satisfying
the JWP can be transformed into a function represented as the sum of two
quadratic M-convex functions, which can be minimized in polynomial time via an
M-convex intersection algorithm if the value oracle of each M-convex function
is given. In this paper, we give an algorithmic answer to a natural question:
What binary finite-valued CSP instances can be represented as the sum of two
quadratic M-convex functions and can be solved in polynomial time via an
M-convex intersection algorithm? We solve this problem by devising a
polynomial-time algorithm for obtaining a concrete form of the representation
in the representable case. Our result presents a larger tractable class of
binary finite-valued CSPs, which properly contains the JWP class.Comment: Full version of a STACS'18 pape
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