Computational Optimization and Applications
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On NCP-Functions
Computational Optimization and Applications - Tập 13 - Trang 201-220 - 1999
In this paper we reformulate several NCP-functions for the nonlinear
complementarity problem (NCP) from their merit function forms and study some
important properties of these NCP-functions. We point out that some of these
NCP-functions have all the nice properties investigated by Chen, Chen and Kanzow
[2] for a modified Fischer-Burmeister function, while some other NCP-functions
may lose one or s...
A study of progressive hedging for stochastic integer programming
Computational Optimization and Applications - Tập 86 - Trang 989-1034 - 2023
Motivated by recent literature demonstrating the surprising effectiveness of the
heuristic application of progressive hedging (PH) to stochastic mixed-integer
programming (SMIP) problems, we provide theoretical support for the inclusion of
integer variables, bridging the gap between theory and practice. We provide
greater insight into the following observed phenomena of PH as applied to SMIP
where...
A Heuristic for Moment-Matching Scenario Generation
Computational Optimization and Applications - Tập 24 - Trang 169-185 - 2003
In stochastic programming models we always face the problem of how to represent
the random variables. This is particularly difficult with multidimensional
distributions. We present an algorithm that produces a discrete joint
distribution consistent with specified values of the first four marginal moments
and correlations. The joint distribution is constructed by decomposing the
multivariate proble...
Using approximate secant equations in limited memory methods for multilevel unconstrained optimization
Computational Optimization and Applications - Tập 51 - Trang 967-979 - 2011
The properties of multilevel optimization problems defined on a hierarchy of
discretization grids can be used to define approximate secant equations, which
describe the second-order behavior of the objective function. Following earlier
work by Gratton and Toint (2009) we introduce a quasi-Newton method (with a
linesearch) and a nonlinear conjugate gradient method that both take advantage
of this n...
An alternating structured trust region algorithm for separable optimization problems with nonconvex constraints
Computational Optimization and Applications - Tập 57 - Trang 365-386 - 2013
In this paper, we propose a structured trust-region algorithm combining with
filter technique to minimize the sum of two general functions with general
constraints. Specifically, the new iterates are generated in the Gauss-Seidel
type iterative procedure, whose sizes are controlled by a trust-region type
parameter. The entries in the filter are a pair: one resulting from feasibility;
the other res...
A constrained optimization reformulation and a feasible descent direction method for $$L_{1/2}$$ regularization
Computational Optimization and Applications - Tập 59 - Trang 263-284 - 2014
In this paper, we first propose a constrained optimization reformulation to the
$$L_{1/2}$$ regularization problem. The constrained problem is to minimize a
smooth function subject to some quadratic constraints and nonnegative
constraints. A good property of the constrained problem is that at any feasible
point, the set of all feasible directions coincides with the set of all
linearized feasible d...
TRESNEI, a Matlab trust-region solver for systems of nonlinear equalities and inequalities
Computational Optimization and Applications - - 2010
The Matlab implementation of a trust-region Gauss-Newton method for
bound-constrained nonlinear least-squares problems is presented. The solver,
called TRESNEI, is adequate for zero and small-residual problems and handles the
solution of nonlinear systems of equalities and inequalities. The structure and
the usage of the solver are described and an extensive numerical comparison with
functions fro...
$${\text {B}}$$ -subdifferentials of the projection onto the matrix simplex
Computational Optimization and Applications - Tập 80 - Trang 915-941 - 2021
An important tool in matrix optimization problems is the strong semismoothness
of the projection mapping onto the cone of real symmetric positive semidefinite
matrices, and the explicit formula for its $${\text {B}}$$
(ouligand)-subdifferentials. In this paper, we examine the corresponding results
for the so-called matrix simplex, that is, the set of real symmetric positive
semidefinite matrices w...
A Trust Region SQP Algorithm for Equality Constrained Parameter Estimation with Simple Parameter Bounds
Computational Optimization and Applications - Tập 28 - Trang 51-86 - 2004
We describe a new algorithm for a class of parameter estimation problems, which
are either unconstrained or have only equality constraints and bounds on
parameters. Due to the presence of unobservable variables, parameter estimation
problems may have non-unique solutions for these variables. These can also lead
to singular or ill-conditioned Hessians and this may be responsible for slow or
non-con...
A comparison of reduced and unreduced KKT systems arising from interior point methods
Computational Optimization and Applications - Tập 68 - Trang 1-27 - 2017
We address the iterative solution of KKT systems arising in the solution of
convex quadratic programming problems. Two strictly related and well established
formulations for such systems are studied with particular emphasis on the effect
of preconditioning strategies on their relation. Constraint and augmented
preconditioners are considered, and the choice of the augmentation matrix is
discussed. ...
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