In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objectivefunction...
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In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objectivefunction has Lipschitz continuous gradient, then we prove that our method obtains an I mu-optimal solution in iterations, where n is the number of blocks. For the class of problems with cheap coordinate derivatives we show that the new method is faster than methods based on full-gradient information. Analysis for the rate of convergence in probability is also provided. For strongly convex functions our method converges linearly. Extensive numerical tests confirm that on very large problems, our method is much more numerically efficient than methods based on full gradient information.
Industrial parks have the trend to be designed to operate as microgrids with renewable distributed generations and battery storage. In this paper, an energy management system is proposed for AC/DC microgrids. This pap...
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The paper describes the ongoing development of optimisation methods for layout design of equi-block n-aspcct mass transit signalling systems. The authors previously applied genetic algorithms (GAs) in place of convent...
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The paper describes the ongoing development of optimisation methods for layout design of equi-block n-aspcct mass transit signalling systems. The authors previously applied genetic algorithms (GAs) in place of conventional gradient search methods for solving the problem. Being theoretically and empirically sound for providing multiple-point search, the GA-based approach simplifies the gradient search approach, broadens the scope for dealing with changes of either the objectivefunction or signalling scheme, and provides robust and global convergence in complex search spaces. The GA-based formulation divides an inter-station run into three sections: a constraint section, a stretchable section and a critical section. Since each of these sections was prescribed with a different design criterion, the OA optimises separately the layout of block joints in each section and their positions within each section. The solution lime for optimal signalling design is further reduced with the use of differential evolution (DE) algorithms. The DE-based method combines the three subordinate objectivefunctions in the original GA algorithm into one composite objective function for one single search. The performance improvements of the DE algorithms over the GA-based method are shown. The choice of variants for solving the DE-based signalling design problem is also discussed.
A quadratic programming method is described for studying simultaneous sum and difference synthesis compromises, and establishing performance bounds, under the restriction of a two-section array feed network. A composi...
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A quadratic programming method is described for studying simultaneous sum and difference synthesis compromises, and establishing performance bounds, under the restriction of a two-section array feed network. A composite objective function is minimised, subject to a union of separate sets of sidelobe constraints, for the sum and difference modes of operation, to avoid a conflicting constraint set. Examples are given to illustrate the principal features of the method.
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