Solving Mathematical Programs with Equilibrium Constraints as Nonlinear Programming: A New Framework

We present a new framework for the solution of mathematical programs with equilibrium constraints (MPECs). In this algorithmic framework, an MPECs is viewed as a concentration of an unconstrained optimization which minimizes the complementarity measure and a nonlinear programming with general constraints. A strategy generalizing ideas of Byrd-Omojokun's trust region method is used to compute steps. By penalizing the tangential constraints into the objective function, we circumvent the problem of not satisfying MFCQ. A trust-funnel-like strategy is used to balance the improvements on feasibility and optimality. We show that, under MPEC-MFCQ, if the algorithm does not terminate in finite steps, then at least one accumulation point of the iterates sequence is an S-stationary point

A globally convergent SQP-type method with least constraint violation for nonlinear semidefinite programming

We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a subproblem based on a local model of infeasibility is formulated to determine a corrective step. In the second phase, a search direction that moves toward optimality is computed by minimizing a local model of the objective function. Importantly, regardless of the feasibility of the original problem, the iterative sequence generated by our proposed method converges to a Fritz-John point of a transformed problem, wherein the constraint violation is minimized. Numerical experiments have been conducted on various complex scenarios to demonstrate the effectiveness of our approach.Comment: 34 page

Performance optimization for energy-aware adaptive checkpointing in embedded real-time systems

Using additional store-checkpoinsts (SCPs) and compare-checkpoints (CCPs), we present an adaptive checkpointing for double modular redundancy (DMR) in this paper. The proposed approach can dynamically adjust the checkpoint intervals. We also design methods to calculate the optimal numbers of checkpoints, which can minimize the average execution time of tasks. Further, the adaptive checkpointing is combined with the DVS (dynamic voltage scaling) scheme to achieve energy reduction. Simulation results show that, compared with the previous methods, the proposed approach significantly increases the likelihood of timely task completion and reduces energy consumption in the presence of faults.<br /

Mantle Transition Zone Structure Beneath Northeast Asia From 2‐D Triplicated Waveform Modeling: Implication for a Segmented Stagnant Slab

The structure of the mantle transition zone (MTZ) in subduction zones is essential for understanding subduction dynamics in the deep mantle and its surface responses. We constructed the P (V_p) and SH velocity (V_s) structure images of the MTZ beneath Northeast Asia based on two‐dimensional (2‐D) triplicated waveform modeling. In the upper MTZ, a normal V_p but 2.5% low V_s layer compared with IASP91 are required by the triplication data. In the lower MTZ, our results show a relatively higher‐velocity layer (+2% V_p and −0.5% V_s compared to IASP91) with a thickness of ~140 km and length of ~1,200 km atop the 660‐km discontinuity. Taking this anomaly as the stagnant slab and considering the plate convergence rate of 7–10 cm/year in the western Pacific region during the late Cenozoic, we deduced that the stagnant slab has a subduction age of less than 30 Ma. This suggests that the observed stagnancy of the slab in the MTZ beneath Northeast Asia may have occurred no earlier than the Early Oligocene. From the constraints derived individually on V_p and V_s structures, high V_p/V_s ratios are obtained for the entire MTZ beneath Northeast Asia, which may imply a water‐rich and/or carbonated environment. Within the overall higher‐velocity stagnant slab, a low‐velocity anomaly was further detected, with a width of ~150 km, V_p and V_s reductions of 1% and 3% relative to IASP91. Such a gap may have provided a passage for hot deep mantle materials to penetrate through the thick slab and feed the Changbaishan volcano

Source Mechanism and Rupture Directivity of the 18 May 2009 M_W 4.6 Inglewood, California, Earthquake

On 18 May 2009, an M_w 4.6 earthquake occurred beneath Inglewood, California, and was widely felt. Though source mechanism and its location suggest that the Newport–Inglewood fault (NIF) may be involved in generating the earthquake, rupture directivity must be modeled to establish the connection between the fault and the earthquake. We first invert for the event’s source mechanism and depth with the cut-and-paste method in the long-period band (>5 s). Because of the low velocity shallow sediments in the Los Angeles (LA) basin, we use two velocity models in the inversion for stations inside and outside the LA basin. However, little difference is observed in the resolved source mechanism (M_w 4.6, strike 246°/145°, dip 50°/77°, rake 17°/138°) and depth (7 to ~9 km), compared to an inversion using the standard southern Calfornia model. With the resolved source parameters, we calibrate the amplitude anomaly of the short-period (0.5–2 Hz) P waves with amplitude adjustment factors (AAF). These AAFs are used as corrections when retrieving source mechanisms of the smaller aftershocks using short-period P waves alone. Most of the aftershocks show similar source mechanisms as that of the mainshock, providing ideal empirical Green’s functions (EGFs) for studying its rupture process. We use a forward modeling approach to retrieve rupture directivity of the mainshock, consistent with movement on the NIF with rupture toward the southeast. Although we focus on P waves for analyzing rupture directivity, the resolved unilateral pattern is also confirmed with the azimuthal variation of the duration of SH waves observed in the basin. The high rupture velocity near the shear velocity and relatively low stress drop are consistent with the hypothesis of rupture on a mature fault