Nickel/Brønsted acid dual-catalyzed regio- and enantioselective hydrophosphinylation of 1,3-dienes: access to chiral allylic phosphine oxides

While chiral allylic organophosphorus compounds are widely utilized in asymmetric catalysis and for accessing bioactive molecules, their synthetic methods are still very limited. We report the development of asymmetric nickel/Brønsted acid dual-catalyzed hydrophosphinylation of 1,3-dienes with phosphine oxides. This reaction is characterized by an inexpensive chiral catalyst, broad substrate scope, and high regio- and enantioselectivity. This study allows the construction of chiral allylic phosphine oxides in a highly economic and efficient manner. Preliminary mechanistic investigations suggest that the 1,3-diene insertion into the chiral Ni–H species is a highly regioselective process and the formation of the chiral C–P bond is an irreversible step.

Asymmetric hydrophosphinylation of 1,3-dienes with phosphine oxides using an inexpensive chiral catalyst has been demonstrated, providing access to chiral allylic phosphine oxides with broad substrate scope and high regio- and enantioselectivity.     

Catalyst-controlled regiodivergent 1,2-difunctionalization of alkenes with two carbon-based electrophiles

Regiodivergent catalysis provides an efficient strategic approach for the construction of architecturally different molecules from the same starting materials. In this field, the intermolecular regiodivergent 1,2-difunctionalization of alkenes with two electrophiles is still a challenging task. A ligand-controlled, nickel-catalyzed regiodivergent dicarbofunctionalization of alkenes using both aryl/vinyl halides and acetals as electrophiles under mild reductive reaction conditions has been accomplished. This study provides a general approach to accessing both β-methoxyl esters and γ-methoxyl esters from readily available acrylates,aryl halides and acetals. Experimental mechanistic evidence supports that the difference in regioselective outcomes is attributed to the ligand tuning the reactivity of the nickel catalyst, which results in different catalytic cycles operating for these two reaction conditions.     

Nickel-catalyzed migratory alkyl–alkyl cross-coupling reaction

The selective cross-coupling of activated electrophiles with unactivated ones has been regarded as a challenging task in cross-electrophile couplings. Herein we describe a migratory cross-coupling strategy, which can overcome this obstacle to access the desired cross-coupling products. Accordingly, a selective migratory cross-coupling of two alkyl electrophiles has been accomplished by nickel catalysis. Remarkably, this alkyl–alkyl cross-coupling reaction provides a platform to prepare 2°–2° carbon–carbon bonds from 1° and 2° carbon coupling partners. Preliminary mechanistic studies suggest that chain-walking occurs at both alkyl halides in this reaction, thus a catalytic cycle with the key step involving two alkylnickel(ii) species is proposed for this transformation.

The selective cross-coupling of activated electrophiles with unactivated ones has been regarded as a challenging task in cross-electrophile couplings.     

Robust Optimization and Data Classification for Characterization of Huntington Disease Onset via Duality Methods

Journal of Optimization Theory and Applications - The features that characterize the onset of Huntington disease (HD) are poorly understood yet have significant implications for research and...     

Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods

In this paper, we study the Kurdyka–?ojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specifically, we develop various calculus rules to deduce the KL exponent of new (possibly nonconvex and nonsmooth) functions formed from functions with known KL exponents. In addition, we show that the well-studied Luo–Tseng error bound together with a mild assumption on the separation of stationary values implies that the KL exponent is \(\frac{1}{2}\). The Luo–Tseng error bound is known to hold for a large class of concrete structured optimization problems, and thus we deduce the KL exponent of a large class of functions whose exponents were previously unknown. Building upon this and the calculus rules, we are then able to show that for many convex or nonconvex optimization models for applications such as sparse recovery, their objective function’s KL exponent is \(\frac{1}{2}\). This includes the least squares problem with smoothly clipped absolute deviation regularization or minimax concave penalty regularization and the logistic regression problem with \(\ell _1\) regularization. Since many existing local convergence rate analysis for first-order methods in the nonconvex scenario relies on the KL exponent, our results enable us to obtain explicit convergence rate for various first-order methods when they are applied to a large variety of practical optimization models. Finally, we further illustrate how our results can be applied to establishing local linear convergence of the proximal gradient algorithm and the inertial proximal algorithm with constant step sizes for some specific models that arise in sparse recovery.     

Characterizing robust set containments and solutions of uncertain linear programs without qualifications

Qualification-free dual characterizations are given for robust polyhedral set containments where a robust counterpart of an uncertain polyhedral set is contained in another polyhedral set or a polyhedral set is contained in a robust counterpart of an uncertain polyhedral set. These results are used to characterize robust solutions of uncertain linear programs, where the uncertainty is defined in terms of intervals or l₁-balls. The hidden separable sub-linearity of the robust counterparts allows qualification-free dual characterizations.     

Error bound results for generalized D-gap functions of nonsmooth variational inequality problems

Solving a variational inequality problem can be equivalently reformulated into solving a unconstraint optimization problem where the corresponding objective function is called a merit function. An important class of merit function is the generalized D-gap function introduced in [N. Yamashita, K. Taji, M. Fukushima, Unconstrained optimization reformulations of variational inequality problems, J. Optim. Theory Appl. 92 (1997) 439-456] and Yamashita and Fukushima (1997) [17]. In this paper, we present new fractional local/global error bound results for the generalized D-gap functions of nonsmooth variational inequality problems, which gives an effective estimate on the distance between a specific point to the solution set, in terms of the corresponding function value of the generalized D-gap function. Numerical examples and a simple application to the free boundary problem are also presented to illustrate the significance of our error bound results.     

A note on alternating projections for ill-posed semidefinite feasibility problems

We observe that Sturm’s error bounds readily imply that for semidefinite feasibility problems, the method of alternating projections converges at a rate of \(\mathcal {O}\Big (k^{-\frac{1}{2^{d+1}-2}}\Big )\), where d is the singularity degree of the problem—the minimal number of facial reduction iterations needed to induce Slater’s condition. Consequently, for almost all such problems (in the sense of Lebesgue measure), alternating projections converge at a worst-case rate of \(\mathcal {O}\Big (\frac{1}{\sqrt{k}}\Big )\).     

Trifluoromethylthiolation of Aryl Iodides and Bromides Enabled by a Bench‐Stable and Easy‐To‐Recover Dinuclear Palladium(I) Catalyst

While palladium catalysis is ubiquitous in modern chemical research, the recovery of the active transition‐metal complex under routine laboratory applications is frequently challenging. Described herein is the concept of alternative cross‐coupling cycles with a more robust (air‐, moisture‐, and thermally‐stable) dinuclear Pd^I complex, thus avoiding the handling of sensitive Pd⁰ species or ligands. Highly efficient C? SCF₃ coupling of a range of aryl iodides and bromides was achieved, and the recovery of the Pd^I complex was accomplished via simple open‐atmosphere column chromatography. Kinetic and computational data support the feasibility of dinuclear Pd^I catalysis. A novel SCF₃‐bridged Pd^I dimer was isolated, characterized by X‐ray crystallography, and verified to be a competent catalytic intermediate.