We propose to use the proximal point algorithm to regularize a "dual" problem of generalized fractional programs (GFP). The proposed technique leads to a new dual algorithm that generates a sequence which co...
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We propose to use the proximal point algorithm to regularize a "dual" problem of generalized fractional programs (GFP). The proposed technique leads to a new dual algorithm that generates a sequence which converges from below to the minimal value of the considered problem. At each step, the proposed algorithm solves approximately an auxiliary problem with a unique dual solution whose every cluster point gives a solution to the dual problem. In the exact minimization case, the sequence of dual solutions converges to an optimal dual solution. For a class of functions, including the linear case, the convergence of the dual values is at least linear.
Assuming unknown target Doppler shift, we focus on robust joint design of the transmit radar waveform and receive Doppler filter bank in the presence of signal-dependent interference. We consider the worst case signal...
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Assuming unknown target Doppler shift, we focus on robust joint design of the transmit radar waveform and receive Doppler filter bank in the presence of signal-dependent interference. We consider the worst case signal-to-interference-plus-noise-ratio (SINR) at the output of the filter bank as the figure of merit to optimize under both a similarity and an energy constraint on the transmit signal. Based on a suitable reformulation of the original non-convex max-min optimization problem, we develop an optimization procedure which monotonically improves the worst-case SINR and converges to a stationary point. Each iteration of the algorithm, involves both a convex and a generalized fractional programming problem which can be globally solved via the generalized dinkelbach's procedure with a polynomial computational complexity. Finally, at the analysis stage, we assess the performance of the new technique versus some counterparts which are available in open literature.
We analyze the convergence of the prox-regularization algorithms introduced in [1], to solve generalized fractional programs, without assuming that the optimal solutions set of the considered problem is nonempty, and ...
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We analyze the convergence of the prox-regularization algorithms introduced in [1], to solve generalized fractional programs, without assuming that the optimal solutions set of the considered problem is nonempty, and since the objective functions are variable with respect to the iterations in the auxiliary problems generated by dinkelbach-type algorithms DT1 and DT2, we consider that the regularizing parameter is also variable. On the other hand we study the convergence when the iterates are only eta(k)-minimizers of the auxiliary problems. This situation is more general than the one considered in [1]. We also give some results concerning the rate of convergence of these algorithms, and show that it is linear and some times superlinear for some classes of functions. Illustrations by numerical examples are given in [1].
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 b...
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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.
In this paper, the problem of solving generalized fractional programs will be addressed. This problem has been extensively studied and several algorithms have been proposed. In this work, we propose an algorithm that ...
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In this paper, the problem of solving generalized fractional programs will be addressed. This problem has been extensively studied and several algorithms have been proposed. In this work, we propose an algorithm that combines the proximal point method with a continuous min-max formulation of discrete generalized fractional programs. The proposed method can handle non-differentiable convex problems with possibly unbounded feasible constraints set, and solves at each iteration a convex program with unique dual solution. It generates two sequences that approximate the optimal value of the considered problem from below and from above at each step. For a class of functions, including the linear case, the convergence rate is at least linear.
We analyse proximal-type minimization methods with generalized Bregman functions by considering a general scheme based on the one studied by Kiwiel [K.C. Kiwiel, Proximal minimization methods with generalized Bregman ...
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We analyse proximal-type minimization methods with generalized Bregman functions by considering a general scheme based on the one studied by Kiwiel [K.C. Kiwiel, Proximal minimization methods with generalized Bregman functions, SIAM J. Control Optim. 35(4) (1997), pp. 1142-1168.] and on successive approximation methods. We apply this scheme to construct methods for generalized fractional programmes.
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