A wide neighborhood interior-point algorithm for linear optimization based on a specific kernel function

This paper presents an interior point algorithm for solving linear optimization problems in a wide neighborhood of the central path introduced by Ai and Zhang (SIAM J Optim 16:400–417, 2005). In each iteration, the algorithm computes the new search directions by using a specific kernel function. The convergence of the algorithm is shown and it is proved that the algorithm has the same iteration bound as the best short-step algorithms. We demonstrate the computational efficiency of the proposed algorithm by testing some Netlib problems in standard form. To best our knowledge, this is the first wide neighborhood path-following interior-point method with the same complexity as the best small neighborhood path-following interior-point methods that uses the kernel function.

     

Capability of Crossed Modules of Lie Algebras

In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module.     

A new infeasible interior-point method based on Darvay’s technique for symmetric optimization

We present a full Nesterov and Todd step primal-dual infeasible interior-point algorithm for symmetric optimization based on Darvay’s technique by using Euclidean Jordan algebras. The search directions are obtained by an equivalent algebraic transformation of the centering equation. The algorithm decreases the duality gap and the feasibility residuals at the same rate. During this algorithm we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main iteration of the algorithm consists of a feasibility step and some centering steps. The starting point in the first iteration of the algorithm depends on a positive number ξ and it is strictly feasible for a perturbed pair. The feasibility steps find strictly feasible iterates for the next perturbed pair. By using centering steps for the new perturbed pair, we obtain strictly feasible iterates close to the central path of the new perturbed pair. The algorithm finds an ?-optimal solution or detects infeasibility of the given problem. Moreover, we derive the currently best known iteration bound for infeasible interior-point methods.     

A Two Phase Free Boundary Problem Related to Quadrature Domains

In this paper we introduce a two phase version of the well-known Quadrature Domain theory, which is a generalized (sub)mean value property for (sub)harmonic functions. In concrete terms, and after reformulation into its PDE version the problem boils down to finding solution to

Simplified infeasible interior-point algorithm for SDO using full Nesterov-Todd step

Interior-point methods for semidefinite optimization problems have been studied frequently, due to their polynomial complexity and practical implications. In this paper we propose a primal-dual infeasible interior-point algorithm that uses full Nesterov-Todd (NT) steps with a different feasibility step. We obtain the currently best known iteration bound for semidefinite optimization problems.     

Carbon‐iodide bond activation by cyclometalated Pt (II) complexes bearing tricyclohexylphosphine ligand: A comparative kinetic study and theoretical elucidation

Cyclometalated Pt (II) complexes [PtMe(C^N)(L)], in which C^N = deprotonated 2,2′‐bipyridine N‐oxide (Obpy), 1 , deprotonated 2‐phenylpyridine (ppy), 2 , deprotonated benzo [h] quinolone (bzq), 3 , and L = tricyclohexylphosphine (PCy₃) were prepared and fully characterized. By treatment of 1–3 with excess MeI, the thermodynamically favored Pt (IV) complexes cis‐[PtMe₂I(C^N)(PCy₃)] (C^N = Obpy, 1a ; ppy, 2a ; and bzq, 3a ) were obtained as the major products in which the incoming methyl and iodine groups adopted cis positions relative to each other. All the complexes were characterized by means of NMR spectroscopy while the absolute configuration of 1a was further determined by X‐ray crystal structure analysis. The reaction of methyl iodide with 1–3 were kinetically explored using UV–vis spectroscopy. On the basis of the kinetic data together with the time‐resolved NMR investigation, it was established that the oxidative addition reaction occurred through the classical S_N2 attack of Pt (II) center on the MeI reagent. Moreover, comparative kinetic studies demonstrated that the electronic and steric nature of either the cyclometalating ligands or the phosphine ligand influence the rate of reaction. Surprisingly, by extending the oxidative addition reaction time, very stable iodine‐bridged Pt (IV)‐Pt (IV) complexes [Pt₂Me₄(C^N)₂(μ‐I)₂] (C^N = Obpy, 1b ; ppy, 2b ; and bzq, 3b ) were obtained and isolated. In order to find a reasonable explanation for the observation, a DFT (density functional theory) computational analysis was undertaken and it was found that the results were consistent with the experimental findings.     

Highly Regioselective and Diastereoselective,One‐Pot,Four‐Component Synthesis of Novel Spiroindenoquinoxalineindolizidine Derivatives

A one‐pot, four‐component procedure for the synthesis of novel spiroindenoquinoxalineindolizidines with high regioselectivity and diastereoselectivity from the 1,3‐dipolar cycloaddition of azomethine ylides, generated from indenoquinoxalines and pipecolinic acid, and chalcones is described. The reaction occurs under reflux of ethanol as a green solvent and in the absence of any catalyst. The cycloadducts are obtained purely without future purification. The regiochemistry and stereochemistry of resultant cycloadducts have been determined by several 2D‐NMR spectroscopic techniques and X‐ray single crystal diffraction.     

An efficient,one-pot,three-component procedure for the synthesis of chiral spirooxindolopyrrolizidines via catalytic highly enantioselective 1,3-dipolar cycloaddition

The catalytic, highly regio-, diastereo-, and enantioselective synthesis of a small library of chiral spirooxindolopyrrolizidines via a three-component 1,3-dipolar cycloaddition reaction of azomethine ylides, derived from isatin, with electron-deficient dipolarophiles, 3-(2-alkenoyl)-1,3-oxazolidin-2-ones, is described. A chiral copper(II) complex of cyclohexane-1,2-bis(arylmethyleneamine) catalyzed this process at room temperature. The reaction mechanism is discussed on the basis of the assignment of the absolute configuration of the cycloadducts.     

‘Click Synthesis’ of Some Novel Benzimidazol Oxime Ethers Containing Heterocycle Residues as Potential ß‐Adrenergic Blocking Agents

The ‘click synthesis’ of some novel O‐substituted oximes, 5a – 5j , which contain heterocycle residues, as new analogs of ß‐adrenoceptor antagonists is described (Scheme 1). The synthesis of these compounds was achieved in four steps. The formation of (E)‐2‐(1H‐benzo[d]imidazol‐1‐yl)‐1‐phenylethanone oxime, followed by their reaction with 2‐(chloromethyl)oxirane, afforded mixture of oil compounds 3 and 4 , which by a subsequent tetra‐n‐butylammonium bromide (TBAB)‐catalyzed reaction with N H heterocycle compounds (Scheme 1), led to the target compounds 5a – 5j in good yields.