Two-sided Constraints Research Articles

Toward Memory-Efficient Analog Design Using Precomputed Lookup Tables

Analog design productivity remains a challenge in the digitally driven semiconductor chip design field. Knowledge-based and simulation-based analog automation approaches have not achieved widespread acceptance in the analog design community. Systematic analog design using precomputed lookup tables (LUTs) is a promising approach that can address the design productivity challenge. Although modern computing systems have powerful memory capabilities, which make the LUT approach viable, reducing the memory footprint of the LUTs remains a challenge. A memory-efficient design technique using LUTs is proposed by using an incomplete grid in the MOSFET degrees-of-freedom (DoFs) space. An efficient indexing technique for the incomplete grid is also proposed, using a precomputed offset array in various scenarios, such as two-sided constraints and three-dimensional LUTs. The results show that the proposed technique can achieve up to a 67% reduction in memory footprint, in addition to improving LUT generation time and query performance.

Limit cycle oscillation and dynamical scenarios in piecewise-smooth nonlinear systems with two-sided constraints

Limit cycle oscillation and dynamical scenarios in piecewise-smooth nonlinear systems with two-sided constraints

Using specularity content to evaluate eight geothermal heat flow maps of Totten Glacier

Abstract. Geothermal heat flow (GHF) is the dominant factor affecting the basal thermal regime of ice sheet dynamics. But it is poorly defined for the Antarctic ice sheet. We compare the basal thermal state of the Totten Glacier catchment as simulated by eight different GHF datasets. We use a basal energy and water flow model coupled with a 3D full-Stokes ice dynamics model to estimate the basal temperature, basal friction heat and basal melting rate. In addition to the location of subglacial lakes, we use specularity content of the airborne radar returns as a two-sided constraint to discriminate between local wet or dry basal conditions and compare the returns with the basal state simulations with different GHFs. Two medium magnitude GHF distribution maps derived from seismic modelling rank well at simulating both cold- and warm-bed regions, the GHFs from Shen et al. (2020) and Shapiro and Ritzwoller (2004). The best-fit simulated result shows that most of the inland bed area is frozen. Only the central inland subglacial canyon, co-located with high specularity content, reaches the pressure melting point consistently in all the eight GHFs. Modelled basal melting rates in the slow-flowing region are generally 0–5 mm yr−1 but with local maxima of 10 mm yr−1 at the central inland subglacial canyon. The fast-flowing grounded glaciers close to the Totten ice shelf are lubricating their bases with meltwater at rates of 10–400 mm yr−1.

Seismic performance of corrugated steel plate shear walls under various constraint conditions

Corrugated steel plate shear walls (CSPSWs) support vertical or horizontal corrugated plates attached to boundary frames through two- or four-sided connections. While two-sided constraints offer better applicability and convenience, this study aims to investigate the seismic behavior of CSPSWs with both two- and four-sided constraints. The investigation considers the coupling effects of direction, aspect ratio, thickness, and axial compression ratio. The study analyzes hysteresis curves, capacity characteristics, stiffness, ductility, and energy consumption for various failure modes. The results indicate that two-sided-constrained specimens exhibit lower mechanical properties compared to four-sided-constrained specimens, especially the initial stiffness. However, both constraint types show X-shaped tension fields diagonally along the CSP under low-cycle reciprocating loading. The horizontal and vertical directions of the corrugated plates have no significant impact on the seismic performance of the four-sided-constrained system, whereas they directly affect the stiffness and lateral load of the two-sided-constrained system. Additionally, an increase in plate thickness results in greater design requirements, particularly for surrounding frame members. Furthermore, when the axial compression ratio does not exceed 0.4, the specimen exhibits good seismic performance and energy dissipation capacity.

Vibro-impact dynamics of an experimental rig with two-sided constraint and bidirectional drift

This paper demonstrates a theoretical and experimental study on a universal vibro-impact system with bidirectional drift. With a dedicated experimental rig that is able to verify numerical simulations, the system has revealed various bifurcations from a piecewise-smooth dynamical model involving impact and dry friction. This experimental rig with a two-sided constraint is designed with adjustable configurations which can be used for experimental testing of versatile piecewise-smooth dynamical systems, e.g., the impact oscillator, the drifting oscillator and the capsule system. It is able to be customised to alter different system parameters, such as friction, number of constraints, mass ratio, impact gap and constraint stiffness, for developing and testing various control strategies. In this paper we particularly studied several types of bifurcations from our preliminary experimental results and discussed the dynamical responses of the system under different excitation frequencies and amplitudes. It was found that with a higher excitation frequency and amplitude, the vibro-impact dynamics on both ends of the constraints could result in a large amount of uncertainties, thus bi-stable and chaotic motions are likely to be observed. While being unstable, the system runs with a relatively high energy efficiency in this configuration.

Numerical simulation of influence of constraint wall configuration on arc characteristics of sheet tungsten electrode

The sheet tungsten electrode is mainly used in ultra-narrow gap TIG welding (UNGW-TIG) because of its shape characteristics, and the constraint wall can further cool and compress the sheet tungsten electrode arc, improve the arc characteristics and optimize the welding process. In this study, the differences between two-sided constraint sheet tungsten electrode arc and all-sided constraint sheet tungsten electrode arc are compared. The results show that the all-sided constraint wall has a better compression effect on the arc. The effects of constraint height and constraint gap on characteristics of all-sided constraint sheet tungsten electrode arc are further discussed. The constraint height mainly improves the effect of compressed arc by increasing the contact area, while the constraint gap mainly improves the effect of compressed arc by increasing the temperature difference. Finally, the temperature distribution in the space of two-sided constraint sheet tungsten electrode arc is measured by electrostatic probe as experimental verification.

Tropical pseudolinear and pseudoquadratic optimization as parametric mean-payoff games

We apply an approach based on parametric mean-payoff games to develop bisection and Newton schemes for solving problems of tropical pseudolinear and pseudoquadratic optimization with general two-sided constraints.

Convex Reformulation for Two-sided Distributionally Robust Chance Constraints with Inexact Moment Information

Constraints on each node and line in power systems generally have upper and lower bounds, denoted as two-sided constraints. Most existing power system optimization methods with the distributionally robust (DR) chance-constrained program treat the two-sided DR chance constraint separately, which is an inexact approximation. This letter derives an equivalent reformulation for the generic two-sided DR chance constraint under the interval moment based ambiguity set, which does not require the exact moment information. The derived reformulation is a second-order cone program (SOCP) formulation and is then applied to the optimal power flow (OPF) problem under uncertainty. Numerical results on several IEEE systems demonstrate the effectiveness of the proposed SOCP formulation and show the differences with other DR chance-constrained OPF approaches.

Fast algorithm for quadratic knapsack problem

The paper considers a quadratic programming problem with a strictly convex separable objective function, a single linear constraint, and two-sided constraints on variables. This problem is commonly called the Convex Knapsack Separable Quadratic Problem, or CKSQP for short. We are interested in an algorithm for solving CKSQP with a linear time complexity. The papers devoted to this topic contain inaccuracies in the description of algorithms and ineffective implementations. In this work, the existing difficulties were overcome.

Influence of the gap size on the response of a single-degree-of-freedom vibro-impact system with two-sided constraints: Experimental tests and numerical modeling

The large displacements caused by strong earthquakes in base-isolated structures (buildings, bridges, strategic facilities, equipment, ⋯) can excessively deform or damage the isolation system or lead to pounding with surrounding moat walls or adjacent structures, if the available seismic gap is not sufficient. The acceleration spikes caused by the impact can damage the structure itself as well as sensitive equipment housed in it. A possible mitigation measure consists in the interposition of deformable shock absorbers (bumpers). In this paper, the influence of the gap amplitude on the experimental response of a single-degree-of-freedom oscillator, excited by a harmonic base acceleration and symmetrically constrained by two unilateral deformable and dissipative bumpers, is investigated. The parametric investigation considered both positive, null, and negative gaps. Particular attention is paid to the study of the effect, on the system response, of the transition from positive to small negative gaps and of excessive negative gaps. Secondary resonances in the low frequency range, associated with the occurrence of multiple impacts, were experimentally observed for small positive gaps. Finally, the experimental results were reproduced, in a sufficiently accurate manner, using a suitable numerical model, whose parameters were identified based on the experimental data.

Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints

The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams.

A Bfgs Method for the Problem of Building S-Shaped Curve

We consider the application of the BFGS method (Broyden, Fletcher, Goldfarb, Shanno) and its projective version L-BFGS-B for minimization of nonlinear function, which corresponds to finding solutions to a system of five nonlinear equations. Among them three equations are integral and depend on unknown parameters of integrands and unknown upper bounds for definite integrals. This system represents the problem of building an S-shaped curve in natural parameterization, which passes through the two given points with given tangents inclination angles and provides a given tangent inclination angle at an intermediate point with a given abscissa. The tangent inclination angle at the point with known abscissa is used to control the inflection point of the S-shaped curve, by which a fragment of the external contour of the Frankl nozzle is modeled.The material of the article is presented in three sections. Section 1 describes a system of five nonlinear equations and analyses its properties related to the existence of many solutions. In section 2 the optimization problem with a non-smooth objective function and linear constraints is presented, the global minima of which correspond to solutions of a system of nonlinear equations. There also is described the application of the modification of r-algorithm to find global minima of the optimization problem.Section 3 describes the application of BFGS and L-BFGS-B methods to find local minima of smooth functions corresponding to finding solutions of a system of nonlinear equations. We formulate two optimization problems with smooth objective functions and two-sided constraints on variables and describe the results of computational experiments for finding solution of the system of nonlinear equations, presented in Section 1, by S-shaped curve. It is shown that BFGS and L-BFGS-B methods are effective if the starting point is selected in such a neighborhood of the minimum point, where the minimized function is approximated fairly accurately by a convex quadratic function.Manuscript received 15.06.2020

Bifurcation analysis of a vibro-impact experimental rig with two-sided constraint

In this paper we carry out an in-depth experimental and numerical investigation of a vibro-impact rig with a two-sided constraint and an external excitation given by a rectangular waveform. The rig, presenting forward and backward drifts, consists of an inner vibrating shaft intermittently impacting with its holding frame. Our interests focus on the multistability and the bifurcation structure observed in the system under two different contacting surfaces. For this purpose, we propose a mathematical model describing the rig dynamics and perform a detailed bifurcation analysis via path-following methods for nonsmooth dynamical systems, using the continuation platform COCO. Our study shows that multistability is produced by the interplay between two fold bifurcations, which give rise to hysteresis in the system. The investigation also reveals the presence of period-doubling bifurcations of limit cycles, which in turn are responsible for the creation of period-2 solutions for which the rig reverses its direction of progression. Furthermore, our study considers a two-parameter bifurcation analysis focusing on directional control, using the period of external excitation and the duty cycle of the rectangular waveform as the main control parameters.

Optimal Portfolio Construction with Two-Sided Weight Constraints and Commission

We consider the optimal portfolio construction problem with two-sided constraints for weights and with commission. The complete algorithmic solution of the problem is given for the Markowitz model (for portfolios without short positions). A heuristic algorithm for solving this problem for the Black’s model (for portfolios with short positions) is proposed.

Optimal program control in the class of quadratic splines for linear systems

This article describes an algorithm for solving the optimal control problem in the case when the considered process is described by a linear system of ordinary differential equations. The initial and final states of the system are fixed and straight two-sided constraints for the control functions are defined. The purpose of optimization is to minimize the quadratic functional of control variables. The control is selected in the class of quadratic splines. There is some evolution of the method when control is selected in the class of piecewise constant functions. Conveniently, due to the addition/removal of constraints in knots, the control function can be piecewise continuous, continuous, or continuously differentiable. The solution algorithm consists in reducing the control problem to a convex mixed-integer quadratically-constrained programming problem, which could be solved by using well-known optimization methods that utilize special software.

Studniarski's derivatives and efficiency conditions for constrained vector equilibrium problems with applications

This article is devoted to the investigation of a vector equilibrium problem involving equality, inequality and set constraints with nonsmooth functions via the higher-order Studniarski derivatives. Under the suitable constraint qualifications, higher-order Karush-Kuhn-Tucker type necessary efficiency conditions for the local weak efficient solutions of a constrained vector equilibrium problem are given. Under suitable assumptions on the objective and constraint functions, the higher-order Karush-Kuhn-Tucker type necessary optimality conditions for local weak efficient solutions become the sufficient conditions. As applications, we obtain the first-order and higher-order optimality conditions for the local weak efficient solutions of a constrained vector variational inequality problem, a constrained vector optimization problem and a transportation problem with two-sided constraints on supplies or demands in terms of Studniarski's derivatives. Several examples are also provided to illustrate the results of the paper.

New constraints on Lorentz Invariance violation from Crab Nebula spectrum beyond 100\xa0TeV

Recently two collaborations, Tibet and HAWC, presented new measurements of gamma-ray spectrum from Crab Nebula (Amenomori et al. in Phys Rev Lett 123(5):051101, 2019, arXiv:1906.05521 [astro-ph.HE]; Abeysekara et al. [HAWC Collaboration] in Astrophys. J. 881, 134, (2019), arXiv:1905.12518 [astro-ph.HE]) which continues beyond 100 TeV. We use these data to establish two-sided constraints on parameters of Lorentz Invariance violation in quantum electrodynamics. The limits on Lorentz violating mass scale for quartic dispersion relation are 4.1times 10^{14}, text{ GeV } (photon splitting) and 1.9times 10^{13}, text{ GeV } (photon decay) for superluminal case, and 1.4times 10^{12} GeV (suppression of shower formation) for subluminal case.

Bounded Perturbations of Nonlinear Discrete Systems: Estimation of Impact and Minimization

The problem of minimizing the impact of bounded perturbations on certain classes of controlled nonlinear discrete systems is solved. The radius of the invariant set, an analog of variance for the perturbations of probabilistic nature, is taken as a measure of the impact. The cases of two-sided linear and nonlinear constraints that form multivalued mappings and also the case in which the nonlinear function has a given estimate of the norm are considered.

A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint

In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the sparsity of the involved matrices and solves the problem via solving a sequence of positive definite system of linear equations after identifying suitable generalized eigenvalues. Specifically, we analyze how to recognize hard case (case 2) in a preprocessing step, fixing an error in Sect. 2.2.2 of Pong and Wolkowicz (Comput Optim Appl 58(2):273–322, 2014) which studies the same problem with the two-sided constraint. Some numerical experiments are given to show the effectiveness of the proposed method and to compare it with some recent algorithms in the literature.

A Note on Tropical Linear and Integer Programs

We present a new, simple compact proof of the known strong duality theorem of tropical linear programming with one-sided constraints. This result together with properties of subeigenvectors enables us to directly solve a special tropical linear program with two-sided constraints. We also study the duality gap in tropical integer linear programming. A direct solution is available for the primal problem. An algorithm of quadratic complexity is presented for the dual problem. A direct solution is available provided that all coefficients of the objective function are integer. This solution provides a good estimate of the optimal objective function value in the general case.