In this paper, we present epsilon-optimality criteria for convex programming problems associated with exact penalty functions. Several authors have given various criteria under the assumption that such convexproblems...
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In this paper, we present epsilon-optimality criteria for convex programming problems associated with exact penalty functions. Several authors have given various criteria under the assumption that such convexproblems and the associated dual problems can be solved. We assume the solvability of neither the convex problem nor the dual problem. To derive our criteria, we estimate the size of the penalty parameter in terms of an epsilon-solution for the dual problem.
We show, using elementary considerations, that a modified barrier function method for the solution of convex programming problems converges for any fixed positive setting of the barrier parameter. With mild conditions...
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We show, using elementary considerations, that a modified barrier function method for the solution of convex programming problems converges for any fixed positive setting of the barrier parameter. With mild conditions on the primal and dual feasible regions, we show how to use the modified barrier function method to obtain primal and dual optimal solutions, even in the presence of degeneracy. We illustrate the argument for convergence in the case of linear programming, and then generalize it to the convexprogramming case.
A proposed incremental model for the solution of a general class of convex programming problems is introduced. The model is an extension of that developed by Mahmoud et al. (1993) which is limited to linear constraint...
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A proposed incremental model for the solution of a general class of convex programming problems is introduced. The model is an extension of that developed by Mahmoud et al. (1993) which is limited to linear constraints having nonzero free coefficients. In the present model, this limitation is relaxed, and allowed to be zero. The model is extended to accommodate those constraints of zero free coefficients. The proposed model is applied to solve the elasto-static contact problems as a class of variation inequality problems of convex nature. A set of different physical nature verification examples is solved and discussed in this paper.
In this study, the authors study simultaneous wireless information and power transfer for multiuser multiple-input-single-output secure multicasting channels with imperfect channel state information. First, a robust s...
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In this study, the authors study simultaneous wireless information and power transfer for multiuser multiple-input-single-output secure multicasting channels with imperfect channel state information. First, a robust secure beamforming design is considered, where the transmit power is minimised subject to the secrecy rate outage probability constraint for legitimate users and the harvested energy outage probability constraint for energy harvesting receivers. The original problem is non-convex due to the presence of the probabilistic constraints. By utilising Bernstein-type inequalities, the authors transform the outage constraints into the deterministic forms. In order to identify a local optimal rank-one solution, the authors propose an efficient approach based on a constrained concave convex procedure method to convert the original problem into a sequence of convex programming problems. Finally, simulation results are provided to validate the performance of the proposed design methods.
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