13,716 research outputs found
A new algorithm for generalized fractional programs
A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual†to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual†parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual†approach is less influenced by scaling.fractional programming;generalized fractional programming;Dinkelbach-type algorithms;quasiconvexity;Karush-Kuhn-Tucker conditions;duality
Super-Resolution in Phase Space
This work considers the problem of super-resolution. The goal is to resolve a
Dirac distribution from knowledge of its discrete, low-pass, Fourier
measurements. Classically, such problems have been dealt with parameter
estimation methods. Recently, it has been shown that convex-optimization based
formulations facilitate a continuous time solution to the super-resolution
problem. Here we treat super-resolution from low-pass measurements in Phase
Space. The Phase Space transformation parametrically generalizes a number of
well known unitary mappings such as the Fractional Fourier, Fresnel, Laplace
and Fourier transforms. Consequently, our work provides a general super-
resolution strategy which is backward compatible with the usual Fourier domain
result. We consider low-pass measurements of Dirac distributions in Phase Space
and show that the super-resolution problem can be cast as Total Variation
minimization. Remarkably, even though are setting is quite general, the bounds
on the minimum separation distance of Dirac distributions is comparable to
existing methods.Comment: 10 Pages, short paper in part accepted to ICASSP 201
Globally Optimal Energy-Efficient Power Control and Receiver Design in Wireless Networks
The characterization of the global maximum of energy efficiency (EE) problems
in wireless networks is a challenging problem due to the non-convex nature of
investigated problems in interference channels. The aim of this work is to
develop a new and general framework to achieve globally optimal solutions.
First, the hidden monotonic structure of the most common EE maximization
problems is exploited jointly with fractional programming theory to obtain
globally optimal solutions with exponential complexity in the number of network
links. To overcome this issue, we also propose a framework to compute
suboptimal power control strategies characterized by affordable complexity.
This is achieved by merging fractional programming and sequential optimization.
The proposed monotonic framework is used to shed light on the ultimate
performance of wireless networks in terms of EE and also to benchmark the
performance of the lower-complexity framework based on sequential programming.
Numerical evidence is provided to show that the sequential fractional
programming framework achieves global optimality in several practical
communication scenarios.Comment: Accepted for publication in the IEEE Transactions on Signal
Processin
A Practical Guide to Robust Optimization
Robust optimization is a young and active research field that has been mainly
developed in the last 15 years. Robust optimization is very useful for
practice, since it is tailored to the information at hand, and it leads to
computationally tractable formulations. It is therefore remarkable that
real-life applications of robust optimization are still lagging behind; there
is much more potential for real-life applications than has been exploited
hitherto. The aim of this paper is to help practitioners to understand robust
optimization and to successfully apply it in practice. We provide a brief
introduction to robust optimization, and also describe important do's and
don'ts for using it in practice. We use many small examples to illustrate our
discussions
A new algorithm for generalized fractional programs
A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual” parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual” approach is less influenced by scaling
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