Γ-robust linear complementarity problems with ellipsoidal uncertainty sets

We study uncertain linear complementarity problems (LCPs), that is, problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Γ-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon Krebs and Schmidt (2020). There, we studied Γ-robustified LCPs for ?₁- and box-uncertainty sets, whereas we now focus on ellipsoidal uncertainty sets. For uncertainty in q or M, we derive conditions for the tractability of the robust counterparts. For these counterparts, we also give conditions for the existence and uniqueness of their solutions. Finally, a case study for the uncertain traffic equilibrium problem is considered, which illustrates the effects of the values of Γ on the feasibility and quality of the respective robustified solutions.     

The second-order cone eigenvalue complementarity problem

The eigenvalue complementarity problem (EiCP) differs from the traditional eigenvalue problem in that the primal and dual variables belong to a closed and convex cone K and its dual, respectively, and satisfy a complementarity condition. In this paper we investigate the solution of the second-order cone EiCP (SOCEiCP) where K is the Lorentz cone. We first show that the SOCEiCP reduces to a special Variational Inequality Problem on a compact set defined by K and a normalization constraint. This guarantees that SOCEiCP has at least one solution, and a new enumerative algorithm is introduced for finding a solution to this problem. The method is based on finding a global minimum of an appropriate nonlinear programming (NLP) formulation of the SOCEiCP using a special branching scheme along with a local nonlinear optimizer that computes stationary points on subsets of the feasible region of NLP associated with the nodes generated by the algorithm. A semi-smooth Newton's method is combined with this enumerative algorithm to enhance its numerical performance. Our computational experience illustrates the efficacy of the proposed techniques in practice.     

A first-order multigrid method for bound-constrained convex optimization

The aim of this paper is to design an efficient multigrid method for constrained convex optimization problems arising from discretization of some underlying infinite dimensional problems. Due to problem dependency of this approach, we only consider bound constraints with (possibly) a single equality constraint. As our aim is to target large-scale problems, we want to avoid computation of second derivatives of the objective function, thus excluding Newton-like methods. We propose a smoothing operator that only uses first-order information and study the computational efficiency of the resulting method.     

Resource Complementarity and IT Economies of Scale: Mechanisms and Empirical Evidence

ABSTRACT

In this study, we explore economies of scale for IT infrastructure and application services. An in-depth appreciation of economies of scale is imperative for an adequate understanding of the impact of IT investments. Our findings indicate that even low IT spending organizations can make a difference by devoting at least 60% of their total IT budget on IT infrastructure in order to foster economies of scale and extract strategic benefits.     

A monotone Newton multisplitting method for the nonlinear complementarity problem with a nonlinear source term

In this paper, we develop a Newton multisplitting method for the nonlinear complementarity problem with a nonlinear source term in which the multisplitting method is used as secondary iterations to approximate the solutions for the resulting linearized subproblems. We prove the monotone convergence theorem for the proposed method under proper conditions.     

融合风光出力场景生成的多能互补微网系统优化配置

多能互补系统结构及设备耦合关系复杂,为提高含高渗透率新能源的多能系统的能源利用效率和运营效益,对考虑风光出力不确定性和相关性的多能互补微网系统优化配置问题进行了研究。在规划阶段充分考虑新能源随机性与相关性,提出了基于核密度估计和Copula理论的风光出力场景生成方法,得到典型日风光出力序列;基于能量枢纽,建立结构完善的含风光多能互补系统的多能流平衡方程,进而以年化总成本最低和一次能源节约率最高为目标建立配置与运行相结合的多能互补系统的双层优化配置模型,并采用智能优化算法对模型进行求解。算例验证和灵敏度分析表明,所述方法能够在考虑风光出力不确定性的基础上得到结构完善的多能互补微网系统优化配置方案,有效降低了多能系统总成本并提高了一次能源节约率。     

非线性互补问题的光滑算法

基于非线性互补问题(NCP(F))的等价变形,利用Fischer-Burmeister函数的光滑逼近函数将非线性互补问题转化为优化问题.提出了一种求解非线性互补问题的光滑逼近算法,通过构造非线性互补问题的一个新的光滑逼近函数,将非线性互补问题等价地转化为求解光滑方程组问题.在一定条件下证明了该算法的全局收敛性.数值实验结果说明了算法的有效性.     

一类弱非线性互补问题的模系矩阵多分裂迭代算法

针对一类求解弱非线性互补问题,提出了模系矩阵多分裂迭代算法。通过变量变换,利用互补向量的性质,将互补问题转化为一类与其等价的不动点方程组。在此基础上,建立一种快速、有效的模系矩阵多分裂迭代算法,并分析了算法的收敛性。数值实验证明了算法的有效性。     

求解互补问题的极大熵和声搜索算法*

针对传统算法无法获得互补问题的多个最优解的困难, 提出了求解互补问题的和声搜索算法。利用NCP函数, 将互补问题转换为一个非光滑方程组问题,用极大熵函数对其进行光滑换处理,进而把互补问题的求解转化为无约束优化,利用和声搜索算法对其进行求解。该算法对目标函数的解析性质没有要求且容易实现,数值结果表明了该方法在求解互补问题中的有效性。