global optimality
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2022 ◽  
Vol 8 (1) ◽  
Author(s):  
Tailong Xiao ◽  
Jianping Fan ◽  
Guihua Zeng

AbstractParameter estimation is a pivotal task, where quantum technologies can enhance precision greatly. We investigate the time-dependent parameter estimation based on deep reinforcement learning, where the noise-free and noisy bounds of parameter estimation are derived from a geometrical perspective. We propose a physical-inspired linear time-correlated control ansatz and a general well-defined reward function integrated with the derived bounds to accelerate the network training for fast generating quantum control signals. In the light of the proposed scheme, we validate the performance of time-dependent and time-independent parameter estimation under noise-free and noisy dynamics. In particular, we evaluate the transferability of the scheme when the parameter has a shift from the true parameter. The simulation showcases the robustness and sample efficiency of the scheme and achieves the state-of-the-art performance. Our work highlights the universality and global optimality of deep reinforcement learning over conventional methods in practical parameter estimation of quantum sensing.


Author(s):  
Christian Füllner ◽  
Steffen Rebennack

AbstractWe propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). We call this algorithm non-convex nested Benders decomposition (NC-NBD). NC-NBD is based on solving dynamically improved mixed-integer linear outer approximations of the MINLP, obtained by piecewise linear relaxations of nonlinear functions. Those MILPs are solved to global optimality using an enhancement of nested Benders decomposition, in which regularization, dynamically refined binary approximations of the state variables and Lagrangian cut techniques are combined to generate Lipschitz continuous non-convex approximations of the value functions. Those approximations are then used to decide whether the approximating MILP has to be dynamically refined and in order to compute feasible solutions for the original MINLP. We prove that NC-NBD converges to an $$\varepsilon $$ ε -optimal solution in a finite number of steps. We provide promising computational results for some unit commitment problems of moderate size.


Author(s):  
Lars Schewe ◽  
Martin Schmidt ◽  
Johannes Thürauf

AbstractThe European gas market is implemented as an entry-exit system, which aims to decouple transport and trading of gas. It has been modeled in the literature as a multilevel problem, which contains a nonlinear flow model of gas physics. Besides the multilevel structure and the nonlinear flow model, the computation of so-called technical capacities is another major challenge. These lead to nonlinear adjustable robust constraints that are computationally intractable in general. We provide techniques to equivalently reformulate these nonlinear adjustable constraints as finitely many convex constraints including integer variables in the case that the underlying network is tree-shaped. We further derive additional combinatorial constraints that significantly speed up the solution process. Using our results, we can recast the multilevel model as a single-level nonconvex mixed-integer nonlinear problem, which we then solve on a real-world network, namely the Greek gas network, to global optimality. Overall, this is the first time that the considered multilevel entry-exit system can be solved for a real-world sized network and a nonlinear flow model.


2022 ◽  
Vol 12 (1) ◽  
pp. 93
Author(s):  
Jutamas Kerdkaew ◽  
Rabian Wangkeeree ◽  
Rattanaporn Wangkeeree

<p style='text-indent:20px;'>In this paper, a robust optimization problem, which features a maximum function of continuously differentiable functions as its objective function, is investigated. Some new conditions for a robust KKT point, which is a robust feasible solution that satisfies the robust KKT condition, to be a global robust optimal solution of the uncertain optimization problem, which may have many local robust optimal solutions that are not global, are established. The obtained conditions make use of underestimators, which were first introduced by Jayakumar and Srisatkunarajah [<xref ref-type="bibr" rid="b1">1</xref>,<xref ref-type="bibr" rid="b2">2</xref>] of the Lagrangian associated with the problem at the robust KKT point. Furthermore, we also investigate the Wolfe type robust duality between the smooth uncertain optimization problem and its uncertain dual problem by proving the sufficient conditions for a weak duality and a strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. The results on robust duality theorems are established in terms of underestimators. Additionally, to illustrate or support this study, some examples are presented.</p>


Micromachines ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 38
Author(s):  
Libin Huang ◽  
Qike Li ◽  
Yan Qin ◽  
Xukai Ding ◽  
Meimei Zhang ◽  
...  

This study designed an in-plane resonant micro-accelerometer based on electrostatic stiffness. The accelerometer adopts a one-piece proof mass structure; two double-folded beam resonators are symmetrically distributed inside the proof mass, and only one displacement is introduced under the action of acceleration, which reduces the influence of processing errors on the performance of the accelerometer. The two resonators form a differential structure that can diminish the impact of common-mode errors. This accelerometer realizes the separation of the introduction of electrostatic stiffness and the detection of resonant frequency, which is conducive to the decoupling of accelerometer signals. An improved differential evolution algorithm was developed to optimize the scale factor of the accelerometer. Through the final elimination principle, excellent individuals are preserved, and the most suitable parameters are allocated to the surviving individuals to stimulate the offspring to find the globally optimal ability. The algorithm not only maintains the global optimality but also reduces the computational complexity of the algorithm and deterministically realizes the optimization of the accelerometer scale factor. The electrostatic stiffness resonant micro-accelerometer was fabricated by deep dry silicon-on-glass (DDSOG) technology. The unloaded resonant frequency of the accelerometer resonant beam was between 24 and 26 kHz, and the scale factor of the packaged accelerometer was between 54 and 59 Hz/g. The average error between the optimization result and the actual scale factor was 7.03%. The experimental results verified the rationality of the structural design.


2021 ◽  
Vol 7 ◽  
Author(s):  
Ryohei Uemura ◽  
Hiroki Akehashi ◽  
Kohei Fujita ◽  
Izuru Takewaki

A method for global simultaneous optimization of oil, hysteretic and inertial dampers is proposed for building structures using a real-valued genetic algorithm and local search. Oil dampers has the property that they can reduce both displacement and acceleration without significant change of natural frequencies and hysteretic dampers possess the characteristic that they can absorb energy efficiently and reduce displacement effectively in compensation for the increase of acceleration. On the other hand, inertial dampers can change (prolong) the natural periods with negative stiffness and reduce the effective input and the maximum acceleration in compensation for the increase of deformation. By using the proposed simultaneous optimization method, structural designers can select the best choice of these three dampers from the viewpoints of cost and performance indices (displacement, acceleration). For attaining the global optimal solution which cannot be attained by the conventional sensitivity-based approach, a method including a real-valued genetic algorithm and local search is devised. In the first stage, a real-valued genetic algorithm is used for searching an approximate global optimal solution. Then a local search procedure is activated for enhancing the optimal character of the solutions by reducing the total quantity of three types of dampers. It is demonstrated that a better design from the viewpoint of global optimality can be obtained by the proposed method and the preference of damper selection strongly depends on the design target (displacement, acceleration). Finally, a multi-objective optimization for the minimum deformation and acceleration is investigated.


2021 ◽  
pp. 1-13
Author(s):  
Sahana Upadhya ◽  
Michael J. Wagner

Abstract A recent increase in the integration of renewable energy systems in existing power grids along with a lack of integrated dispatch models has led to waste in power produced. This paper presents a mixed-integer nonlinear optimization model for hybrid renewable-generator-plus-battery systems, with the objective of maximizing long-term profit. Prior studies have revealed that both high and low state of charge (SOC) of the battery is detrimental to its lifetime and results in reduced battery capacity over time. In addition, increased number of cycles of charge and discharge also causes capacity reduction. This paper models these two factors with a constraint relating capacity loss to the SOC and number of cycles completed by the battery. Loss in capacity is penalized in the objective function of the optimization model, thereby disincentivizing high and low SOCs and frequent cycling. A rolling time horizon optimization approach is used to overcome the computational difficulties of achieving global optimality within a long-term time horizon. By incorporating battery degradation, the model is capable of maximizing the profits from the power dispatch to the grid while also maximizing the life of the battery. This paper exercises the model within a case study using a sample photovoltaic system generation time series that considers multiple battery capacities. The results indicate that the optimal battery lifetime is extended in comparison to conventional models that ignore battery degradation in dispatch decisions. Finally, we analyze the relationship between battery operational decisions and the resultant capacity fade.


2021 ◽  
Vol 7 (10) ◽  
pp. 198
Author(s):  
Mattia Litrico ◽  
Sebastiano Battiato ◽  
Sotirios A. Tsaftaris ◽  
Mario Valerio Giuffrida

This paper proposes a novel approach for semi-supervised domain adaptation for holistic regression tasks, where a DNN predicts a continuous value y∈R given an input image x. The current literature generally lacks specific domain adaptation approaches for this task, as most of them mostly focus on classification. In the context of holistic regression, most of the real-world datasets not only exhibit a covariate (or domain) shift, but also a label gap—the target dataset may contain labels not included in the source dataset (and vice versa). We propose an approach tackling both covariate and label gap in a unified training framework. Specifically, a Generative Adversarial Network (GAN) is used to reduce covariate shift, and label gap is mitigated via label normalisation. To avoid overfitting, we propose a stopping criterion that simultaneously takes advantage of the Maximum Mean Discrepancy and the GAN Global Optimality condition. To restore the original label range—that was previously normalised—a handful of annotated images from the target domain are used. Our experimental results, run on 3 different datasets, demonstrate that our approach drastically outperforms the state-of-the-art across the board. Specifically, for the cell counting problem, the mean squared error (MSE) is reduced from 759 to 5.62; in the case of the pedestrian dataset, our approach lowered the MSE from 131 to 1.47. For the last experimental setup, we borrowed a task from plant biology, i.e., counting the number of leaves in a plant, and we ran two series of experiments, showing the MSE is reduced from 2.36 to 0.88 (intra-species), and from 1.48 to 0.6 (inter-species).


Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2355
Author(s):  
Faïçal Ndaïrou ◽  
Delfim F. M. Torres

Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall type inequality as well as results on continuity and differentiability of perturbed trajectories. Moreover, a Mangasarian type sufficient global optimality condition for the general analytic kernel fractional optimal control problem is proved. An illustrative example is discussed.


Author(s):  
S. Lämmel ◽  
V. Shikhman

AbstractWe study sparsity constrained nonlinear optimization (SCNO) from a topological point of view. Special focus will be on M-stationary points from Burdakov et al. (SIAM J Optim 26:397–425, 2016), also introduced as $$N^C$$ N C -stationary points in Pan et al. (J Oper Res Soc China 3:421–439, 2015). We introduce nondegenerate M-stationary points and define their M-index. We show that all M-stationary points are generically nondegenerate. In particular, the sparsity constraint is active at all local minimizers of a generic SCNO. Some relations to other stationarity concepts, such as S-stationarity, basic feasibility, and CW-minimality, are discussed in detail. By doing so, the issues of instability and degeneracy of points due to different stationarity concepts are highlighted. The concept of M-stationarity allows to adequately describe the global structure of SCNO along the lines of Morse theory. For that, we study topological changes of lower level sets while passing an M-stationary point. As novelty for SCNO, multiple cells of dimension equal to the M-index are needed to be attached. This intriguing fact is in strong contrast with other optimization problems considered before, where just one cell suffices. As a consequence, we derive a Morse relation for SCNO, which relates the numbers of local minimizers and M-stationary points of M-index equal to one. The appearance of such saddle points cannot be thus neglected from the perspective of global optimization. Due to the multiplicity phenomenon in cell-attachment, a saddle point may lead to more than two different local minimizers. We conclude that the relatively involved structure of saddle points is the source of well-known difficulty if solving SCNO to global optimality.


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