On the Linear Convergence to Weak/Standard d-Stationary Points of DCA-Based Algorithms for Structured Nonsmooth DC Programming

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

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Enhancement of the transverse thermoelectric conductivity originating from stationary points in nodal lines

Physical Review B ◽

10.1103/physrevb.102.205128 ◽

2020 ◽

Vol 102 (20) ◽

Author(s):

Susumu Minami ◽

Fumiyuki Ishii ◽

Motoaki Hirayama ◽

Takuya Nomoto ◽

Takashi Koretsune ◽

...

Keyword(s):

Stationary Points ◽

Nodal Lines

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Direct Kinetic Measurements and Master Equation Modelling of the Unimolecular Decomposition of Resonantly-Stabilized CH2CHCHC(O)OCH3 Radical and an Upper Limit Determination for CH2CHCHC(O)OCH3 + O2 Reaction

Zeitschrift für Physikalische Chemie ◽

10.1515/zpch-2020-1612 ◽

2020 ◽

Vol 234 (7-9) ◽

pp. 1251-1268 ◽

Cited By ~ 1

Author(s):

Satya Prakash Joshi ◽

Prasenjit Seal ◽

Timo Theodor Pekkanen ◽

Raimo Sakari Timonen ◽

Arrke J. Eskola

Keyword(s):

Master Equation ◽

Density Functional ◽

Rate Coefficient ◽

Decomposition Kinetics ◽

Basis Sets ◽

Stationary Points ◽

Unimolecular Decomposition ◽

Kinetic Measurements ◽

Point Energy ◽

Upper Limit

AbstractMethyl-Crotonate (MC, (E)-methylbut-2-enoate, CH3CHCHC(O)OCH3) is a potential component of surrogate fuels that aim to emulate the combustion of fatty acid methyl ester (FAME) biodiesels with significant unsaturated FAME content. MC has three allylic hydrogens that can be readily abstracted under autoignition and combustion conditions to form a resonantly-stabilized CH2CHCHC(O)OCH3 radical. In this study we have utilized photoionization mass spectrometry to investigate the O2 addition kinetics and thermal unimolecular decomposition of CH2CHCHC(O)OCH3 radical. First we determined an upper limit for the bimolecular rate coefficient of CH2CHCHC(O)OCH3 + O2 reaction at 600 K (k ≤ 7.5 × 10−17 cm3 molecule−1 s−1). Such a small rate coefficient suggest this reaction is unlikely to be important under combustion conditions and subsequent efforts were directed towards measuring thermal unimolecular decomposition kinetics of CH2CHCHC(O)OCH3 radical. These measurements were performed between 750 and 869 K temperatures at low pressures (<9 Torr) using both helium and nitrogen bath gases. The potential energy surface of the unimolecular decomposition reaction was probed at density functional (MN15/cc-pVTZ) level of theory and the electronic energies of the stationary points obtained were then refined using the DLPNO-CCSD(T) method with the cc-pVTZ and cc-pVQZ basis sets. Master equation simulations were subsequently carried out using MESMER code along the kinetically important reaction pathway. The master equation model was first optimized by fitting the zero-point energy corrected reaction barriers and the collisional energy transfer parameters $\Delta{E_{{\text{down}},\;{\text{ref}}}}$ and n to the measured rate coefficients data and then utilize the constrained model to extrapolate the decomposition kinetics to higher pressures and temperatures. Both the experimental results and the MESMER simulations show that the current experiments for the thermal unimolecular decomposition of CH2CHCHC(O)OCH3 radical are in the fall-off region. The experiments did not provide definite evidence about the primary decomposition products.

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Linear Convergence for Distributed Optimization Without Strong Convexity

2020 59th IEEE Conference on Decision and Control (CDC) ◽

10.1109/cdc42340.2020.9304381 ◽

2020 ◽

Author(s):

Xinlei Yi ◽

Shengjun Zhang ◽

Tao Yang ◽

Tianyou Chai ◽

Karl H. Johansson

Keyword(s):

Distributed Optimization ◽

Linear Convergence ◽

Strong Convexity

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Topological Approach to Mathematical Programs with Switching Constraints

Set-Valued and Variational Analysis ◽

10.1007/s11228-021-00581-5 ◽

2021 ◽

Author(s):

Vladimir Shikhman

Keyword(s):

Stationary Point ◽

Mountain Pass Theorem ◽

Strong Stability ◽

Complete Characterization ◽

Stationary Points ◽

Mathematical Programs ◽

Linear Independence Constraint Qualification ◽

Point Set ◽

Stationary Level

AbstractWe study mathematical programs with switching constraints (for short, MPSC) from the topological perspective. Two basic theorems from Morse theory are proved. Outside the W-stationary point set, continuous deformation of lower level sets can be performed. However, when passing a W-stationary level, the topology of the lower level set changes via the attachment of a w-dimensional cell. The dimension w equals the W-index of the nondegenerate W-stationary point. The W-index depends on both the number of negative eigenvalues of the restricted Lagrangian’s Hessian and the number of bi-active switching constraints. As a consequence, we show the mountain pass theorem for MPSC. Additionally, we address the question if the assumption on the nondegeneracy of W-stationary points is too restrictive in the context of MPSC. It turns out that all W-stationary points are generically nondegenerate. Besides, we examine the gap between nondegeneracy and strong stability of W-stationary points. A complete characterization of strong stability for W-stationary points by means of first and second order information of the MPSC defining functions under linear independence constraint qualification is provided. In particular, no bi-active Lagrange multipliers of a strongly stable W-stationary point can vanish.

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