9,104 research outputs found
Algorithms for the continuous nonlinear resource allocation problem---new implementations and numerical studies
Patriksson (2008) provided a then up-to-date survey on the
continuous,separable, differentiable and convex resource allocation problem
with a single resource constraint. Since the publication of that paper the
interest in the problem has grown: several new applications have arisen where
the problem at hand constitutes a subproblem, and several new algorithms have
been developed for its efficient solution. This paper therefore serves three
purposes. First, it provides an up-to-date extension of the survey of the
literature of the field, complementing the survey in Patriksson (2008) with
more then 20 books and articles. Second, it contributes improvements of some of
these algorithms, in particular with an improvement of the pegging (that is,
variable fixing) process in the relaxation algorithm, and an improved means to
evaluate subsolutions. Third, it numerically evaluates several relaxation
(primal) and breakpoint (dual) algorithms, incorporating a variety of pegging
strategies, as well as a quasi-Newton method. Our conclusion is that our
modification of the relaxation algorithm performs the best. At least for
problem sizes up to 30 million variables the practical time complexity for the
breakpoint and relaxation algorithms is linear
Using a conic bundle method to accelerate both phases of a quadratic convex reformulation
We present algorithm MIQCR-CB that is an advancement of method
MIQCR~(Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving
mixed-integer quadratic programs and works in two phases: the first phase
determines an equivalent quadratic formulation with a convex objective function
by solving a semidefinite problem , and, in the second phase, the
equivalent formulation is solved by a standard solver. As the reformulation
relies on the solution of a large-scale semidefinite program, it is not
tractable by existing semidefinite solvers, already for medium sized problems.
To surmount this difficulty, we present in MIQCR-CB a subgradient algorithm
within a Lagrangian duality framework for solving that substantially
speeds up the first phase. Moreover, this algorithm leads to a reformulated
problem of smaller size than the one obtained by the original MIQCR method
which results in a shorter time for solving the second phase.
We present extensive computational results to show the efficiency of our
algorithm
A Primal-Dual Augmented Lagrangian
Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both the primal and the dual variables simultaneously. A benefit of this approach is that the quality of the dual variables is monitored explicitly during the solution of the subproblem. Moreover, each subproblem may be regularized by imposing explicit bounds on the dual variables. Two primal-dual variants of conventional primal methods are proposed: a primal-dual bound constrained Lagrangian (pdBCL) method and a primal-dual 1 linearly constrained Lagrangian (pd1-LCL) method
-Box Optimization for Green Cloud-RAN via Network Adaptation
In this paper, we propose a reformulation for the Mixed Integer Programming
(MIP) problem into an exact and continuous model through using the -box
technique to recast the binary constraints into a box with an sphere
constraint. The reformulated problem can be tackled by a dual ascent algorithm
combined with a Majorization-Minimization (MM) method for the subproblems to
solve the network power consumption problem of the Cloud Radio Access Network
(Cloud-RAN), and which leads to solving a sequence of Difference of Convex (DC)
subproblems handled by an inexact MM algorithm. After obtaining the final
solution, we use it as the initial result of the bi-section Group Sparse
Beamforming (GSBF) algorithm to promote the group-sparsity of beamformers,
rather than using the weighted -norm. Simulation results
indicate that the new method outperforms the bi-section GSBF algorithm by
achieving smaller network power consumption, especially in sparser cases, i.e.,
Cloud-RANs with a lot of Remote Radio Heads (RRHs) but fewer users.Comment: 4 pages, 4 figure
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