This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are glob...This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.展开更多
For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initi...For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.展开更多
A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent ...A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.展开更多
For unconstrained optimization, a new hybrid projection algorithm is presented m the paper. This algorithm has some attractive convergence properties. Convergence theory can be obtained under the condition that Δ↓f...For unconstrained optimization, a new hybrid projection algorithm is presented m the paper. This algorithm has some attractive convergence properties. Convergence theory can be obtained under the condition that Δ↓f（x） is uniformly continuous. If Δ↓f（x） is continuously differentiable pseudo-convex, the whole sequence of iterates converges to a solution of the problem without any other assumptions. Furthermore, under appropriate conditions one shows that the sequence of iterates has a cluster-point if and only if Ω＊ ≠ θ. Numerical examples are given at the end of this paper.展开更多
文摘This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.
基金Project(2021JLM-49) supported by Natural Science Basic Research Program of Shaanxi-Joint Fund of Hanjiang to Weihe River Valley Water Diversion Project,ChinaProject(42077248) supported by the National Natural Science Foundation of China
文摘For deep tunnel projects,selecting an appropriate initial support distance is critical to improving the self-supporting capacity of surrounding rock.In this work,an intuitive method for determining the tunnel’s initial support distance was proposed.First,based on the convergence-confinement method,a three-dimensional analytical model was constructed by combining an analytical solution of a non-circular tunnel with the Tecplot software.Then,according to the integral failure criteria of rock,the failure tendency coefficients of hard surrounding rock were computed and the spatial distribution plots of that were constructed.On this basis,the tunnel’s key failure positions were identified,and the relationship between the failure tendency coefficient at key failure positions and their distances from the working face was established.Finally,the distance from the working face that corresponds to the critical failure tendency coefficient was taken as the optimal support distance.A practical project was used as an example,and a reasonable initial support distance was successfully determined by applying the developed method.Moreover,it is found that the stability of hard surrounding rock decreases rapidly within the range of 1.0D(D is the tunnel diameter)from the working face,and tends to be stable outside the range of 1.0D.
文摘A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.
基金This work is supported by National Natural Science Foundation under Grants No. 10571106 and 10471159.
文摘For unconstrained optimization, a new hybrid projection algorithm is presented m the paper. This algorithm has some attractive convergence properties. Convergence theory can be obtained under the condition that Δ↓f（x） is uniformly continuous. If Δ↓f（x） is continuously differentiable pseudo-convex, the whole sequence of iterates converges to a solution of the problem without any other assumptions. Furthermore, under appropriate conditions one shows that the sequence of iterates has a cluster-point if and only if Ω＊ ≠ θ. Numerical examples are given at the end of this paper.
