A shaped beam synthesis methodology for planar arrays with control of the ripple amplitude in the shaped region, and constraints on the sidelobe and cross-polar levels, is proposed in this paper. A previously develope...
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A shaped beam synthesis methodology for planar arrays with control of the ripple amplitude in the shaped region, and constraints on the sidelobe and cross-polar levels, is proposed in this paper. A previously developed synthesis formulation for designing finite impulse response (FIR) filters by transforming a nonconvex synthesis problem to a convex optimization scheme enforcing conjugate symmetric excitation weights, is extended to real and coupled radiating elements of complex geometry, taking into account mutual coupling effects. The optimization procedure is integrated with a finite array approach simulating different array environments. This approach is based on the infinite array model through a Floquet modal- and general scattering matrix (GSM)-based analysis, where the periodic radiating element is characterized from a hybrid and full-wave analysis procedure combining the FEM, modal analysis, and domain decomposition technique. Numerical results of different synthesized beam patterns are presented for arrays of open-ended apertures and microstrip antennas.
A finite-dimensional mathematical programming problem with convex data and inequality constraints is considered. A suitable definition of condition number is obtained via canonical perturbations of the given problem, ...
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A finite-dimensional mathematical programming problem with convex data and inequality constraints is considered. A suitable definition of condition number is obtained via canonical perturbations of the given problem, assuming uniqueness of the optimal solutions. The distance among mathematical programming problems is defined as the Lipschitz constant of the difference of the corresponding Kojima functions. It is shown that the distance to ill-conditioning is bounded above and below by suitable multiples of the reciprocal of the condition number, thereby generalizing the classical Eckart-Young theorem. A partial extension to the infinite-dimensional setting is also obtained.
We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, respectively. We provide also an exam...
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We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, respectively. We provide also an example of a convex optimization problem for which the classical generalized interior-point conditions given so far in the literature cannot be applied, while the one given by us is applicable. By using a technique developed by Magnanti, we derive some duality results for the optimization problem with cone constraints and its Lagrange dual problem, and we show that a duality result recently given in the literature for this pair of problems has self-contradictory assumptions.
Hyperbolic polynomials have their origins in partial differential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p...
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Hyperbolic polynomials have their origins in partial differential equations. We show in this paper that they have applications in interior point methods for convex programming. Each homogeneous hyperbolic polynomial p has an associated open and convex cone called its hyperbolicity cone. We give an explicit representation of this cone in terms of polynomial inequalities. The function F(x) = -log p(x) is a logarithmically homogeneous self-concordant barrier function for the hyperbolicity cone with barrier parameter equal to the degree of p. The function F(x) possesses striking additional properties that are useful in designing long-step interior point methods. For example, we show that the long-step primal potential reduction methods of Nesterov and Todd and the surface-following methods of Nesterov and Nemirovskii extend to hyperbolic barrier functions. We also show that there exists a hyperbolic barrier function on every homogeneous cone.
A dual algorithm for problems of Fourier Synthesis is proposed. Partially finite convex programming provides tools for a formulation which enables to elude static pixelization of the object to be reconstructed. This l...
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A dual algorithm for problems of Fourier Synthesis is proposed. Partially finite convex programming provides tools for a formulation which enables to elude static pixelization of the object to be reconstructed. This leads to a regularized reconstruction-interpolation formula for problems in which finitely many and possibly irregularly spaced samples of the Fourier transform of the unknown object are known, as is the case in Magnetic Resonance Imaging with non-Cartesian and sparse acquisitions. (C) 2008 Elsevier Ltd. All rights reserved.
Consideration was given to the methods of optimal correction of the improper problems of convex programming based on the Lagrange function regularized in both variables. The methods are independent of the kind of impr...
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Consideration was given to the methods of optimal correction of the improper problems of convex programming based on the Lagrange function regularized in both variables. The methods are independent of the kind of impropriety of the original problem. Approximation precision was estimated, and the relation of this approach to the existing methods of regularization of the incorrect extremal problems was discussed.
This paper presents a neural network approach for solving convex programming problems with equality constraints. After defining the energy function and neural dynamics of the proposed neural network, we show the exist...
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This paper presents a neural network approach for solving convex programming problems with equality constraints. After defining the energy function and neural dynamics of the proposed neural network, we show the existence of an equilibrium point at which the neural dynamics becomes asymptotically stable. It is shown that under proper conditions, an optimal solution of the underlying convex programming problems is an equilibrium point of the neural dynamics, and vise verse. The configuration of the proposed neural network with an exact layout is provided for solving linear programming problems. The operational characteristics of the neural network are demonstrated by numerical examples. (C) 1998 Elsevier Science Ltd. All rights reserved.
After a brief survey on condition numbers for linear systems of equalities, we analyse error bounds for convex functions and convex sets. The canonical representation of a convex set is defined. Other representations ...
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After a brief survey on condition numbers for linear systems of equalities, we analyse error bounds for convex functions and convex sets. The canonical representation of a convex set is defined. Other representations of a convex set by a convex function are compared with the canonical representation. Then, condition numbers are introduced for convex sets and their convex representations.
We consider a multiple-block separable convex programming problem, where the objective function is the sum of m individual convex functions without overlapping variables, and the constraints are linear, aside from sid...
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We consider a multiple-block separable convex programming problem, where the objective function is the sum of m individual convex functions without overlapping variables, and the constraints are linear, aside from side constraints. Based on the combination of the classical Gauss-Seidel and the Jacobian decompositions of the augmented Lagrangian function, we propose a partially parallel splitting method, which differs from existing augmented Lagrangian based splitting methods in the sense that such an approach simplifies the iterative scheme significantly by removing the potentially expensive correction step. Furthermore, a relaxation step, whose computational cost is negligible, can be incorporated into the proposed method to improve its practical performance. Theoretically, we establish global convergence of the new method in the framework of proximal point algorithm and worst-case nonasymptotic O(1/t) convergence rate results in both ergodic and nonergodic senses, where t counts the iteration. The efficiency of the proposed method is further demonstrated through numerical results on robust PCA, i.e., factorizing from incomplete information of an unknown matrix into its low-rank and sparse components, with both synthetic and real data of extracting the background from a corrupted surveillance video.
Sliding modes are used to analyze a class of dynamical systems that solve convex programming problems. The analysis is carried out using concepts from the theory of differential equations with discontinuous right-hand...
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Sliding modes are used to analyze a class of dynamical systems that solve convex programming problems. The analysis is carried out using concepts from the theory of differential equations with discontinuous right-hand sides and Lyapunov stability theory. It is shown that the equilibrium points of the system coincide with the minimizers of the convex programming problem, and that irrespective of the initial state of the system the state trajectory converges to the solution set of the problem. The dynamic behavior of the systems is illustrated by two numerical examples.
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