In several array synthesis problems the Pack of a common element pattern among different antennas makes the use of classical synthesis methods based on the array factor questionable. A recently introduced approach to ...
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In several array synthesis problems the Pack of a common element pattern among different antennas makes the use of classical synthesis methods based on the array factor questionable. A recently introduced approach to array synthesis is exploited to take account in an exact fashion of the mutual coupling between patches for the synthesis of pencil beams by microstrip arrays. Optimality of the approach allows quantifying the advantages of the method with respect to common approaches, which largely compensates in several cases for its additional computational burden.
We discuss some properties of the distance to infeasibility of a conic linear system Ax = b, x is an element of C, where C is a closed convex cone. Some interesting connections between the distance to infeasibility an...
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We discuss some properties of the distance to infeasibility of a conic linear system Ax = b, x is an element of C, where C is a closed convex cone. Some interesting connections between the distance to infeasibility and the solution of certain optimization problems are established. Such connections provide insight into the estimation of the distance to infeasibility and the explicit computation of infeasible perturbations of a given system. We also investigate the properties of the distance to infeasibility assuming that the perturbations are restricted to have a particular structure. Finally, we extend most of our results to more general conic systems Ax + b is an element of C-Y, x is an element of C-X, where C-X and C-Y are closed, convex cones.
We exhibit useful properties of proximal bundle methods for finding min(S) f, where f and S are convex. We show that they asymptotically find objective subgradients and constraint multipliers involved in optimality co...
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We exhibit useful properties of proximal bundle methods for finding min(S) f, where f and S are convex. We show that they asymptotically find objective subgradients and constraint multipliers involved in optimality conditions, multipliers of objective pieces for max-type functions, and primal and dual solutions in Lagrangian decomposition of convex programs. When applied to Lagrangian relaxation of nonconvex programs, they find solutions to relaxed convexified versions of such programs. Numerical results are presented for unit commitment in power production scheduling.
Andersen and Y [Math. programming, 84 (1999), pp. 375-399] suggested a homogeneous formulation and an interior-point algorithm for solution of the monotone complementarity problem ( MCP). The advantage of the homogene...
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Andersen and Y [Math. programming, 84 (1999), pp. 375-399] suggested a homogeneous formulation and an interior-point algorithm for solution of the monotone complementarity problem ( MCP). The advantage of the homogeneous formulation is that it always has a solution. Moreover, in the case in which the MCP is solvable or is (strongly) infeasible, the solution provides a certificate of optimality or infeasibility. In this note we demonstrate that if the suggested formulation is applied to the Karush-Kuhn-Tucker optimality conditions corresponding to a convex optimization problem, then an infeasibility certificate provides information about whether the primal or dual problem is infeasible given certain assumptions.
In this paper we consider an ordinary convex program with no qualification conditions (such as Slater's condition) and for which the optimal set is neither required to be compact, nor to be equal to the sum of a c...
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In this paper we consider an ordinary convex program with no qualification conditions (such as Slater's condition) and for which the optimal set is neither required to be compact, nor to be equal to the sum of a compact set and a linear space. It is supposed only that the infimum alpha is finite. A very wide class of convex functions is exhibited for which the optimum is always attained and alpha is equal to the supremum of the ordinary dual program. Additional results concerning the existence of optimal solutions in the non convex case are also given.
We propose a BFGS primal-dual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generates feasible iterates and consists in computing ...
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We propose a BFGS primal-dual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generates feasible iterates and consists in computing approximate solutions of the optimality conditions perturbed by a sequence of positive parameters mu converging to zero. We prove that it converges q-superlinearly for each fixed mu. We also show that it is globally convergent to the analytic center of the primal-dual optimal set when mu tends to 0 and strict complementarity holds.
Necessary and sufficient conditions are established for the existence of positive solutions to polynomial diophatine equations. A method for computation of the set of positive solutions to polynomial diophatine equati...
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Necessary and sufficient conditions are established for the existence of positive solutions to polynomial diophatine equations. A method for computation of the set of positive solutions to polynomial diophatine equation based on extreme points and extreme directions is proposed. The effectiveness of the method is demonstrated on a numerical example.
Proposed by Tibshirani, the least absolute shrinkage and selection operator (LASSO) estimates a vector of regression coefficients by minimizing the residual sum of squares subject to a constraint on the l(1)-norm of t...
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Proposed by Tibshirani, the least absolute shrinkage and selection operator (LASSO) estimates a vector of regression coefficients by minimizing the residual sum of squares subject to a constraint on the l(1)-norm of the coefficient vector. The LASSO estimator typically has one or more zero elements and thus shares characteristics of both shrinkage estimation and variable selection. In this article we treat the LASSO as a convex programming problem and derive its dual. Consideration of the primal and dual problems together leads to important new insights into the characteristics of the LASSO estimator and to an improved method for estimating its covariance matrix. Using these results we also develop an efficient algorithm for computing LASSO estimates which is usable even in cases where the number of regressors exceeds the number of observations. An S-Plus library based on this algorithm is available from StatLib.
Some Optimal Control problems can be reduce to problems of Nonlinear Progran1ming. Methods of penalty functions are widely used in Nonlinear programming. Theorems of the existence of exact penalty parameters for solvi...
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Some Optimal Control problems can be reduce to problems of Nonlinear Progran1ming. Methods of penalty functions are widely used in Nonlinear programming. Theorems of the existence of exact penalty parameters for solving of the problems of Nonlinear programming by the method of exact penalty functions are proved. The knowledge of any exact penalty parameter permits at once to decide the given problem in the presence of an algorithm of unconditional minimization of a nonsmooth function.
In the present paper some barrier and penalty methods (e.g., logarithmic barriers, SUMT, exponential penalties), which define a continuously differentiable primal and dual path, applied to linearly constrained convex ...
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