37,740 research outputs found
A novel iterative convex approximation method
Abstract—In this paper, we propose a novel iterative convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of successively refined approximate problems, each of which is much easier to solve than the original problem. To achieve convergence, the approximate problem only needs to exhibit a weak form of convexity, namely, pseudo-convexity. We show that the proposed framework not only includes as special cases a number of existing methods, for example, the gradient method and the Jacobi algorithm, but also leads to new algorithms which enjoy easier implementation and faster convergence speed. We also propose a novel line search method for nondifferentiable optimization problems, which is carried out over a properly constructed differentiable function with the benefit of a simpli-fied implementation as compared to state-of-the-art line search techniques that directly operate on the original nondifferentiable objective function. The advantages of the proposed algorithm are shown, both theoretically and numerically, by several ex-ample applications, namely, MIMO broadcast channel capacity computation and LASSO in sparse signal recovery
A Unified Successive Pseudo-Convex Approximation Framework
In this paper, we propose a successive pseudo-convex approximation algorithm
to efficiently compute stationary points for a large class of possibly
nonconvex optimization problems. The stationary points are obtained by solving
a sequence of successively refined approximate problems, each of which is much
easier to solve than the original problem. To achieve convergence, the
approximate problem only needs to exhibit a weak form of convexity, namely,
pseudo-convexity. We show that the proposed framework not only includes as
special cases a number of existing methods, for example, the gradient method
and the Jacobi algorithm, but also leads to new algorithms which enjoy easier
implementation and faster convergence speed. We also propose a novel line
search method for nondifferentiable optimization problems, which is carried out
over a properly constructed differentiable function with the benefit of a
simplified implementation as compared to state-of-the-art line search
techniques that directly operate on the original nondifferentiable objective
function. The advantages of the proposed algorithm are shown, both
theoretically and numerically, by several example applications, namely, MIMO
broadcast channel capacity computation, energy efficiency maximization in
massive MIMO systems and LASSO in sparse signal recovery.Comment: submitted to IEEE Transactions on Signal Processing; original title:
A Novel Iterative Convex Approximation Metho
Partially distributed outer approximation
This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression
Multi-view Metric Learning in Vector-valued Kernel Spaces
We consider the problem of metric learning for multi-view data and present a
novel method for learning within-view as well as between-view metrics in
vector-valued kernel spaces, as a way to capture multi-modal structure of the
data. We formulate two convex optimization problems to jointly learn the metric
and the classifier or regressor in kernel feature spaces. An iterative
three-step multi-view metric learning algorithm is derived from the
optimization problems. In order to scale the computation to large training
sets, a block-wise Nystr{\"o}m approximation of the multi-view kernel matrix is
introduced. We justify our approach theoretically and experimentally, and show
its performance on real-world datasets against relevant state-of-the-art
methods
Iterative learning control for constrained linear systems
This paper considers iterative learning control for linear systems with convex control input constraints. First, the constrained ILC problem is formulated in a novel successive projection framework. Then, based on this projection method, two algorithms are proposed to solve this constrained ILC problem. The results show that, when perfect tracking is possible, both algorithms
can achieve perfect tracking. The two algorithms differ however in that one algorithm needs much less computation than the other. When perfect tracking is not possible, both algorithms can exhibit a form of practical convergence to a "best approximation". The effect of weighting matrices on the performance of the algorithms is also discussed and finally, numerical simulations are given to demonstrate the e®ectiveness of the proposed methods
Spectrum optimization in multi-user multi-carrier systems with iterative convex and nonconvex approximation methods
Several practical multi-user multi-carrier communication systems are
characterized by a multi-carrier interference channel system model where the
interference is treated as noise. For these systems, spectrum optimization is a
promising means to mitigate interference. This however corresponds to a
challenging nonconvex optimization problem. Existing iterative convex
approximation (ICA) methods consist in solving a series of improving convex
approximations and are typically implemented in a per-user iterative approach.
However they do not take this typical iterative implementation into account in
their design. This paper proposes a novel class of iterative approximation
methods that focuses explicitly on the per-user iterative implementation, which
allows to relax the problem significantly, dropping joint convexity and even
convexity requirements for the approximations. A systematic design framework is
proposed to construct instances of this novel class, where several new
iterative approximation methods are developed with improved per-user convex and
nonconvex approximations that are both tighter and simpler to solve (in
closed-form). As a result, these novel methods display a much faster
convergence speed and require a significantly lower computational cost.
Furthermore, a majority of the proposed methods can tackle the issue of getting
stuck in bad locally optimal solutions, and hence improve solution quality
compared to existing ICA methods.Comment: 33 pages, 7 figures. This work has been submitted for possible
publicatio
Toward Energy Efficient Multiuser IRS-Assisted URLLC Systems: A Novel Rank Relaxation Method
This paper proposes an energy efficient resource allocation design algorithm
for an intelligent reflecting surface (IRS)-assisted downlink ultra-reliable
low-latency communication (URLLC) network. This setup features a multi-antenna
base station (BS) transmitting data traffic to a group of URLLC users with
short packet lengths. We maximize the total network's energy efficiency (EE)
through the optimization of active beamformers at the BS and passive
beamformers (a.k.a. phase shifts) at the IRS. The main non-convex problem is
divided into two sub-problems. An alternating optimization (AO) approach is
then used to solve the problem. Through the use of the successive convex
approximation (SCA) with a novel iterative rank relaxation method, we construct
a concave-convex objective function for each sub-problem. The first sub-problem
is a fractional program that is solved using the Dinkelbach method and a
penalty-based approach. The second sub-problem is then solved based on
semi-definite programming (SDP) and the penalty-based approach. The iterative
solution gradually approaches the rank-one for both the active beamforming and
unit modulus IRS phase-shift sub-problems. Our results demonstrate the efficacy
of the proposed solution compared to existing benchmarks
Multicast Multigroup Beamforming for Per-antenna Power Constrained Large-scale Arrays
Large in the number of transmit elements, multi-antenna arrays with
per-element limitations are in the focus of the present work. In this context,
physical layer multigroup multicasting under per-antenna power constrains, is
investigated herein. To address this complex optimization problem
low-complexity alternatives to semi-definite relaxation are proposed. The goal
is to optimize the per-antenna power constrained transmitter in a maximum
fairness sense, which is formulated as a non-convex quadratically constrained
quadratic problem. Therefore, the recently developed tool of feasible point
pursuit and successive convex approximation is extended to account for
practical per-antenna power constraints. Interestingly, the novel iterative
method exhibits not only superior performance in terms of approaching the
relaxed upper bound but also a significant complexity reduction, as the
dimensions of the optimization variables increase. Consequently, multicast
multigroup beamforming for large-scale array transmitters with per-antenna
dedicated amplifiers is rendered computationally efficient and accurate. A
preliminary performance evaluation in large-scale systems for which the
semi-definite relaxation constantly yields non rank-1 solutions is presented.Comment: submitted to IEEE SPAWC 2015. arXiv admin note: substantial text
overlap with arXiv:1406.755
Energy efficiency optimization in MIMO interference channels: A successive pseudoconvex approximation approach
In this paper, we consider the (global and sum) energy efficiency
optimization problem in downlink multi-input multi-output multi-cell systems,
where all users suffer from multi-user interference. This is a challenging
problem due to several reasons: 1) it is a nonconvex fractional programming
problem, 2) the transmission rate functions are characterized by
(complex-valued) transmit covariance matrices, and 3) the processing-related
power consumption may depend on the transmission rate. We tackle this problem
by the successive pseudoconvex approximation approach, and we argue that
pseudoconvex optimization plays a fundamental role in designing novel iterative
algorithms, not only because every locally optimal point of a pseudoconvex
optimization problem is also globally optimal, but also because a descent
direction is easily obtained from every optimal point of a pseudoconvex
optimization problem. The proposed algorithms have the following advantages: 1)
fast convergence as the structure of the original optimization problem is
preserved as much as possible in the approximate problem solved in each
iteration, 2) easy implementation as each approximate problem is suitable for
parallel computation and its solution has a closed-form expression, and 3)
guaranteed convergence to a stationary point or a Karush-Kuhn-Tucker point. The
advantages of the proposed algorithm are also illustrated numerically.Comment: submitted to IEEE Transactions on Signal Processin
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