求解含储能装置的微电网动态最优潮流的对偶半定规划方法

电网动态最优潮流是一个全天24个时间断面耦合的最优潮流问题,需要考虑常规机组爬坡率约束和分布式储能装置能量约束。具有二阶收敛特性的内点法可以对其进行快速求解,但无法保证解的全局最优性。采用对偶半定规划法求解该问题,对孤岛运行的微电网动态最优潮流原始模型及向对偶半定规划模型的转换做了详细的介绍,并给出了严格的全局最优性判据。同时将储能装置的强非线性模型等价地变换成线性模型,并给出了相应的证明。某实际微电网和IEEE 30节点系统的测试结果表明,对偶半定规划法可高效求解动态最优潮流问题,其解可保证全局最优性。

Duality theorem for smash coproduct over quantum groupoids

The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.

Multiple solutions of Cu-C6H9NaO7 and Ag-C6H9NaO7 nanofluids flow over nonlinear shrinking surface

Model of Casson nanofluid flow over a nonlinear shrinking surface is considered.Model of Tiwari and Das is applied to nanofluid comprising of sodium alginate with copper and silver.The governing nonlinear equations incorporating the effects of the viscous dissipation are transformed into boundary value problems (BVPs) of ordinary differential equations (ODEs) by using appropriate similarity transformations.The resulting equations are converted into initial value problems (IVPs) using the shooting method which are then solved by Runge-Kutta method of fourth order.In order to determine the stability of the dual solutions obtained,stability analysis is performed and discovered that the first (second) solution is stable (unstable) and physically realizable (unrealizable).Both the thickness of the thermal boundary layer as well as temperature increase when the Casson parameter (β) is increased in the second solution.

A Duality Theorem Associated with the Smash Product of Graded Ring and G-set

Let G be a group, HG and R a G graded ring. We study the duality Theorem for G actions and smash products R#G/H of the G graded ring R and the G set G/H.

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.

Constrained Dynamic Game and Symmetric Duality for Variational Problems

A certain constrained dynamic game is shown to be equivalent to a pair of symmetric dual variational problems which have more general formulation than those already existing in the literature. Various duality results are proved under convexity and generalized convexity assumptions on the appropriate functionals. The dynamic game is also viewed as equivalent to a pair of dual variational problems without the condition of fixed points. It is also indicated that the equivalent formulation of a pair of symmetric dual variational problems as dynamic generalization of those had been already studied in the literature. In essence, the purpose of the research is to establish that the solution of variational problems yields the solution of the dynamic game.

Optimality Conditions and Duality for Nondifferentiable Multiobjective Semi-Infinite Programming Problems with Generalized(C,α,ρ,d)-Convexity

This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-type dual model for the nonlinear nondifferentiable multiobjective semiinfinite programming problem and establish weak,strong and strict converse duality theorems relating the primal and the dual problems.

Higher-order Mond-Weir converse duality in multiobjective programming involving cones

In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et al. Higher order duality in inultiobjective programming with cone constraints. Optimization, 2010, 59： 29-43].

SUFFICIENCY AND DUALITY FOR NONSMOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED UNIVEX FUNCTIONS

In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs.

Koszul Differential Graded Algebras and BGG Correspondence II

The concept of Koszul differential graded (DG for short) algebra is introduced in [8].Let A be a Koszul DG algebra.If the Ext-algebra of A is finite-dimensional,i.e.,the trivial module A k is a compact object in the derived category of DG A-modules,then it is shown in [8] that A has many nice properties.However,if the Ext-algebra is infinitedimensional,little is known about A.As shown in [15] (see also Proposition 2.2),A k is not compact if H(A) is finite-dimensional.In this paper,it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality.A DG version of the BGG correspondence is deduced from the Koszul duality theorem.

Second order duality for multiobjective programming with cone constraints

We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.

HIGHER-ORDER DUALITY FOR A CLASS OF NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED TYPE I AND RELATED FUNCTIONS

This paper extends the class of generalized type I functions introduced by Aghezzaf and Hachimi（2000） to the context of higher-order case and formulate a number of higher-order duals to a non-differentiable multi-objective programming problem and establishes higher-order duality results under the higher-order generalized type I functions introduced in the present paper, A special case that appears repeatedly in the literature is that the support function is the square root of a positive semi-definite quadratic form. This and other special cases can be readily generated from these results.

Conjugacy Classes and Characters for Extensions of Finite Groups

Let H be an extension of a finite group Q by a finite group G. Inspired by the results of duality theorems for etale gerbes on orbifolds, the authors describe the number of conjugacy classes of H that map to the same conjugacy class of Q. Furthermore, a generalization of the orthogonality relation between characters of G is proved.

DUALITY FOR A CLASS OF NONS MOOTH MULTIOBJECTIVE PROGRAMMING PROBLEMS

In this paper, two new dual models of nonsmooth multiobjective programmingare constructed and two duality results are derived.

ON CONE D.C. OPTIMIZATION AND CONJUGATE DUALITY

This paper derives first order necessary and sufficient conditions for unconstrained coned.c. Programming problems where the underlined space is partially ordered with respect to acone. These conditions are given in terms of directional derivatives and subdifferentials of thecomponent functions. Moreover, conjugate duality for cone d.c. Optimization is discussed andweak duality theorem is proved in a more general partially ordered linear topological vectorspace (generalizing the results in [11]).

The Presentation Problem of the Conjugate Cone of the Hardy Space Hp(0 < p≤1)

The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).

THE REALIZATION OF MULTIPLIER HILBERT BIMODULE ON BIDUAL SPACE AND TIETZE EXTENSION THEOREM

The multiplier bimodule of Hilbert bimodule is introduced in a way similar to [1], and its realization on a quotient of bidual space and Tietze extension theorem are obtained similar to that in C-algebra case. As a result, the multiplier bimodule here is also a Hilbert bimodule.

Applications of gauge duality in robust principal component analysis and semidefinite programming

Gauge duality theory was originated by Preund （1987）, and was recently further investigated by Friedlander et al. （2014）. When solving some matrix optimization problems via gauge dual, one is usually able to avoid full matrix decompositions such as singular value and/or eigenvalue decompositions. In such an approach, a gauge dual problem is solved in the first stage, and then an optimal solution to the primal problem can be recovered from the dual optimal solution obtained in the first stage. Recently, this theory has been applied to a class of semidefinite programming （SDP） problems with promising numerical results by Friedlander and Mac^to （2016）. We establish some theoretical results on applying the gauge duality theory to robust principal component analysis （PCA） and general SDP. For each problem, we present its gauge dual problem, characterize the optimality conditions for the primal-dual gauge pair, and validate a way to recover a primal optimal solution from a dual one. These results are extensions of Friedlander and Macedo （2016） from nuclear norm regularization to robust PCA and from a special class of SDP which requires the coefficient matrix in the linear objective to be positive definite to SDP problems without this restriction. Our results provide further understanding in the potential advantages and disadvantages of the gauge duality theory.