Second-order Constraints Research Articles

Optimal science-time reorientation policy for the Comet Interceptor flyby via sequential convex programming

This paper introduces an algorithm to perform optimal reorientation of a spacecraft during a high speed flyby mission that maximizes the time a certain target is kept within the field of view of scientific instruments. The method directly handles the nonlinear dynamics of the spacecraft, sun exclusion constraint, torque and momentum limits on the reaction wheels as well as potential faults in these actuators. A sequential convex programming approach was used to reformulate non-convex pointing objectives and other constraints in terms of a series of novel convex cardinality minimization problems. These subproblems were then efficiently solved even on limited hardware resources using convex programming solvers implementing second-order conic constraints. The proposed method was applied to a scenario that involved maximizing the science time for the upcoming Comet Interceptor flyby mission developed by the European Space Agency. Extensive simulation results demonstrate the capability of the approach to generate viable trajectories even in the presence of reaction wheel failures or prior dust particle impacts.

Optimal Operation for Integrated Electricity and Natural Gas Systems Considering Dynamic Gas Linepack

With the increasing penetration of gas-fired turbines, the efficient and safe operation of power systems depends on the sufficient supply of natural gas. Hence, we proposed a coordinated optimal operation model of integrated electricity and natural gas systems (IENs). The gas linepack is considered by applying dynamic flow models. The non-convex Weymouth equality is converted to a second-order cone inequality constraint and a concave constraint that can be linearized by Taylor expansion. The initial operation point is obtained by optimizing the steady flow model. We proposed an algorithm based on the sequential strategy to solve this mixed-integer second order cone programming (MISOCP). The case study demonstrates that the proposed method can solve the MISOCP effectively and the operation cost can be reduced by taking full use of the gas linepack that is calculated by the dynamic gas flow model.

Combining First- and Second-Order Continuity Constraints in Ultrasound Elastography.

Ultrasound elastography is a prominent noninvasive medical imaging technique that estimates tissue elastic properties to detect abnormalities in an organ. A common approximation to tissue elastic modulus is tissue strain induced after mechanical stimulation. To compute tissue strain, ultrasound radio frequency (RF) data can be processed using energy-based algorithms. These algorithms suffer from ill-posedness to tackle. A continuity constraint along with the data amplitude similarity is imposed to obtain a unique solution to the time-delay estimation (TDE) problem. Existing energy-based methods exploit the first-order spatial derivative of the displacement field to construct a regularizer. This first-order regularization scheme alone is not fully consistent with the mechanics of tissue deformation while perturbed with an external force. As a consequence, state-of-the-art techniques suffer from two crucial drawbacks. First, the strain map is not sufficiently smooth in uniform tissue regions. Second, the edges of the hard or soft inclusions are not well-defined in the image. Herein, we address these issues by formulating a novel regularizer taking both first- and second-order derivatives of the displacement field into account. The second-order constraint, which is the principal novelty of this work, contributes both to background continuity and edge sharpness by suppressing spurious noisy edges and enhancing strong boundaries. We name the proposed technique: Second-Order Ultrasound eLastography (SOUL). Comparative assessment of qualitative and quantitative results shows that SOUL substantially outperforms three recently developed TDE algorithms called Hybrid, GLUE, and MPWC-Net++. SOUL yields 27.72%, 62.56%, and 81.37% improvements of the signal-to-noise ratio (SNR) and 72.35%, 54.03%, and 65.17% improvements of the contrast-to-noise ratio (CNR) over GLUE with data pertaining to simulation, phantom, and in vivo tissue, respectively. The SOUL code can be downloaded from code.sonography.ai.

Rapid phonotactic constraint learning in ageing: evidence from speech errors

ABSTRACT Older adults are able to implicitly pick up structural regularities in the environment despite declining cognitive abilities. Here, we investigated elderly’s abilities to implicitly pick up novel linguistic constraints in speech production. Across four training days, young and healthy older Dutch-speaking adults were asked to rapidly recite Dutch phonotactic syllables. Two unrestricted consonants were experimentally constrained to onset or coda positions depending on the medial vowel. Analysis of speech errors revealed rapid adherence to the novel second-order constraints in both the younger and the older group. However, in the older group, there was weaker trial-specific learning compared to the younger group, potentially due to explicit memory deficits. Strikingly, the error pattern of the elderly mirrors earlier developmental work with children using the same paradigm. The findings are discussed in light of possible age-dependent differences in implicit and explicit cognitive subsystems underlying human skill learning.

Second-order efficient optimality conditions for set-valued vector optimization in terms of asymptotic contingent epiderivatives

We propose a generalized second-order asymptotic contingent epiderivative of a set-valued mapping, study its properties, as well as relations to some second-order contingent epiderivatives, and sufficient conditions for its existence. Then, using these epiderivatives, we investigate set-valued optimization problems with generalized inequality constraints. Both second-order necessary conditions and sufficient conditions for optimality of the Karush–Kuhn–Tucker type are established under the second-order constraint qualification. An application to Mond–Weir and Wolfe duality schemes is also presented. Some remarks and examples are provided to illustrate our results.

Semidefinite relaxation method for polynomial optimization with second-order cone complementarity constraints

<p style='text-indent:20px;'>Polynomial optimization problem with second-order cone complementarity constraints (SOCPOPCC) is a special case of mathematical program with second-order cone complementarity constraints (SOCMPCC). In this paper, we consider how to apply Lasserre's type of semidefinite relaxation method to solve SOCPOPCC. To this end, we first reformulate SOCPOPCC equivalently as a polynomial optimization and then solve the reformulated polynomial optimization with semidefinite relaxation method. For a special case of SOCPOPCC, we present another reformulation of polynomial optimization, which is of lower degree. SDP relaxation method is applied to solve the new polynomial optimization. Numerical examples are reported to show the efficiency of our proposed method.</p>

Multi-Timeslots Data Collection With Low Rank and Modified Second-Order Horizontal Total Variation for Wireless Sensor Networks

Decreasing the number of data gathered is the most highly effective way to decrease the power consumption for wireless sensor networks. Compressed Data Gathering, as it known to all, is a data collection method in wireless sensor networks, but it cannot achieve sparse sensing as all data need to be sensed and then transmitted in most practical applications. At the same time, it has been shown the effectiveness of the total variation and low rank constraints in data restoration. In order to enhance the accuracy of data recovery and decrease energy cost in wireless sensor networks, we propose a Multi-Timeslots Data Collection scheme, which includes two aspects: Structure Random Sparse Sampling method and data restoration algorithm with Low Rank and Modified Second-Order Horizontal Total Variation Constraints. By adopting the proposed sampling method, the number of data sensing and transmission is greatly reduced, thereby prolong the network lifetime. We fully exploit temporal stability and low rank characteristics of wireless sensor networks data, and build a temporal-stability based nuclear norm regularization minimization model. Meanwhile, we apply the alternating direction method to solve the problem. The simulation results present that the proposed sampling method has a corresponding enhancement effect on the matrix-completion based data restoration algorithms. In terms of recovery precision, the proposed scheme outperforms the state-of-the-art methods for different types of data in the network. Moreover, with the compression ratio increasing, the proposed scheme can still exactly recover the lost data and the advantages become increasingly obvious.

Expected Utility Maximization with Stochastic Dominance Constraints in Complete Markets

The problem of expected utility maximization with stochastic dominance constraints in complete markets is studied. In the quantile formulation, i.e., changing the decision variable of the problem from a random variable to its quantile function, the problem with a first-order stochastic dominance constraint is easy and can be solved explicitly. For the problem with a second-order stochastic dominance constraint, the optimal solution is characterized explicitly in terms of the solution of a dual problem, which interestingly can be regarded as a problem of two-person efficient risk sharing. Moreover, the optimal solution of the problem of efficient risk sharing is characterized fully and, in some special cases, has closed form.

Pension fund management with investment certificates and stochastic dominance

This paper considers an extension of the common asset universe of a pension fund to investment certificates. Investment certificates are a class of structured products particularly interesting for their special payoff structures and they are acquiring relevancy in the worldwide markets. In fact, some subclasses of certificates offer loss protection and show high liquidity and, thus, they can be very appreciated by pension fund managers. We consider the problem of a pension fund manager who has to implement an Asset and Liability Management model trying to achieve a long-term sustainability. Therefore, we formulate a multi-stage stochastic programming problem adopting a discrete scenario tree and a multi-objective function. We propose a technique to price highly structured products such as investment certificates on a discrete scenario tree. Finally, we solve the investment problem considering some investment certificate types both in term of payoff structure and protection level, and we test whether they are preferred or not to standard hedging contract such as put options. Moreover, we test the inclusion of first-order and second-order stochastic dominance constraints on multiple stages with respect to a benchmark portfolio. Numerical results show that the portfolio composition reacts to the inclusion of the stochastic dominance constraints, and that the optimal portfolio is efficiently able to reach several targets such as liquidity, returns, sponsor’s extraordinary contribution and funding gap.

On the calm b-differentiability of projector onto circular cone and its applications

In this paper, we study a concept on the calm B-differentiability, a new kind of generalized differentiabilities for a given vector function introduced by Ye and Zhou in 2017, of the projector onto the circular cone. Then, we discuss its applications in mathematical programming problems with circular cone complementarity constraints. Here, this problem can be considered to be a generalization of mathematical programming problems with second-order cone complementarity constraints, and thus it includes a large class of mathematical models in optimization theory. Consequently, the obtained results for this problem are generalized, and then corresponding results for some special mathematical problems can be implied from them directly. For more detailed information, we will first prove the calmly B-differentiable property of the projector onto the circular cone. This result is not easy to be shown by simply resorting to those of the projection operator onto the second-order cone. By virtue of exploiting variational techniques, we next establish the exact formula for the regular (Fréchet) normal cone (this concept was proposed by Kruger and Mordukhovich in 1980) to the circular cone complementarity set. Note that this set can be considered to be a generalization of the second-order cone complementarity set. In finally, the exact formula for the regular (Fréchet) normal cone to the circular cone complementarity set would be useful for us to study first-order necessary optimality conditions for mathematical programming problems with circular cone complementarity constraints. Our obtained results in the paper are new, and they are generalized to some existing ones in the literature.

The Geometric Properties of a Class of Nonsymmetric Cones

Geometric methods are important for researching the differential properties of metric projectors, sensitivity analysis, and the augmented Lagrangian algorithm. Sun [3] researched the relationship among the strong second-order sufficient condition, constraint nondegeneracy, B-subdifferential nonsingularity of the KKT system, and the strong regularity of KKT points in investigating nonlinear semidefinite programming problems. Geometric properties of cones are necessary in studying second-order sufficient condition and constraint nondegeneracy. In this paper, we study the geometric properties of a class of nonsymmetric cones, which is widely applied in optimization problems subjected to the epigraph of vector k-norm functions and low-rank-matrix approximations. We compute the polar, the tangent cone, the linear space of the tangent cone, the critical cone, and the affine hull of this critical cone. This paper will support future research into the sensitivity and algorithms of related optimization problems.

Optimality conditions for circular cone complementarity programs

In this paper, we first provide some results on first- and second-order analysis to a circular cone complementary set Γ. In this way, we obtain a parabolical regularity of Γ as well as an exact computation for second epi-derivative of the indicator function to Γ. We then establish first- and second-order optimality conditions for a mathematical programming problem involving a circular cone complementary constraint under the validation of metric subregularity and second-order tangent constraint qualification. Our results are sharpened in comparison with some existing ones in the literature.

A Neural Network Based on the Metric Projector for Solving SOCCVI Problem.

We propose an efficient neural network for solving the second-order cone constrained variational inequality (SOCCVI). The network is constructed using the Karush-Kuhn-Tucker (KKT) conditions of the variational inequality (VI), which is used to recast the SOCCVI as a system of equations by using a smoothing function for the metric projection mapping to deal with the complementarity condition. Aside from standard stability results, we explore second-order sufficient conditions to obtain exponential stability. Especially, we prove the nonsingularity of the Jacobian of the KKT system based on the second-order sufficient condition and constraint nondegeneracy. Finally, we present some numerical experiments, illustrating the efficiency of the neural network in solving SOCCVI problems. Our numerical simulations reveal that, in general, the new neural network is more dominant than all other neural networks in the SOCCVI literature in terms of stability and convergence rates of trajectories to SOCCVI solution.

Subsurface electrical resistivity modelling over a suspected fault zone at Ojirami, Southwestern Nigeria

The subsurface of a suspected fault zone at Ojirami Southwestern Nigeria was investigated using the four-electrode array model of the electrical resistivity method of geophysical prospecting. Measurements were taken along four traverses using the 1-D and 2-D electrical resistivity field techniques. The Schlumberger and dipole–dipole electrode configurations were respectively utilized for each of the techniques. The 1-D data were interpreted by partial curve matching and computer iteration using the IPI2Win® software. The data obtained from the 2-D ERI were processed and migrated using the Dipro for Windows® 4.0 inversion software. Inversion was done using the finite element modelling (FEM) method. The second-order smoothness constraint was used and five iterations were carried out on each data set. Three 2-D resistivity models and one geoelectric section were generated from the inverted resistivity data. A resistivity depth slice map of the depth range of 2.5–5 m was also generated for the assessment of the spatial configuration of the suspected fault zone. Geoelectric units which include the topsoil/outcrop, weathered/faulted bedrock and the fresh bedrock were delineated by the 2-D resistivity models and the geoelectric section. The suspected fault zone manifested as zone of comparatively low resistivity (8–81 Ω-m) within two resistive (800 to > 5000 Ω m) basement bedrocks on the resistivity images and geoelectric section. The resistivity depth slice map also revealed the fault zone to be a low resistivity discontinuity within two flanks of fresh bedrocks. The study concluded that the study area is indeed a fault zone.

Second-order viability problems for differential inclusions with endpoint constraint and duality

ABSTRACT The paper deals with the optimal control of second-order viability problems for differential inclusions with endpoint constraint and duality. Based on the concept of infimal convolution and new approach to convex duality functions, we construct dual problems for discrete and differential inclusions and prove the duality results. It seems that the Euler–Lagrange type inclusions are ‘duality relations’ for both primary and dual problems. Finally, some special cases show the applicability of the general approach; duality in the control problem with second-order polyhedral DFIs and endpoint constraints defined by a polyhedral cone is considered.

An Improved ADMM-Based Distributed Optimal Operation Model of AC/DC Hybrid Distribution Network Considering Wind Power Uncertainties

An increasing share of uncertain distributed generations is being integrated into the ac/dc hybrid distribution network (HDN) with the partitioning characteristic. In this article, we propose a distributed optimization framework where the exchange power is regarded as coupling variables being the consensus on both sides of voltage source converters between ac and dc subnetworks. An improved alternating direction method of multipliers (ADMM) algorithm with the varying penalty parameter is applied to solve the proposed distributed operation problem in ac/dc HDN. In each ac or dc subnetwork, a two-stage distributionally robust optimization (DRO) model for optimal operation is formulated considering wind power uncertainties addressed by 1-norm and ∞-norm based data-driven methods. The DRO model is solved by the column and constraint generation algorithm, where the polyhedral-based linearization method is introduced to approximate the second-order cone power flow constraints with a series of linear constraints to improve the computational speed. Numerical results based on a real-world 152-bus system including three ac subnetworks and two dc subnetworks validate the effectiveness of the proposed method.

Mg2vec: Learning Relationship-Preserving Heterogeneous Graph Representations via Metagraph Embedding

Given that heterogeneous information networks (HIN) encompass nodes and edges belonging to different semantic types, they can model complex data in real-world scenarios. Thus, HIN embedding has received increasing attention, which aims to learn node representations in a low-dimensional space, in order to preserve the structural and semantic information on the HIN. In this regard, metagraphs, which model common and recurring patterns on HINs, emerge as a powerful tool to capture semantic-rich and often latent relationships on HINs. Although metagraphs have been employed to address several specific data mining tasks, they have not been thoroughly explored for the more general HIN embedding. In this paper, we leverage metagraphs to learn relationship-preserving HIN embedding in a self-supervised setting, to support various relationship mining tasks. In particular, we observe that most of the current approaches often under-utilize metagraphs, which are only applied in a pre-processing step and do not actively guide representation learning afterwards. Thus, we propose the novel framework of mg2vec, which learns the embeddings for metagraphs and nodes jointly. That is, metagraphs actively participates in the learning process by mapping themselves to the same embedding space as the nodes do. Moreover, metagraphs guide the learning through both first- and second-order constraints on node embeddings, to model not only latent relationships between a pair of nodes, but also individual preferences of each node. Finally, we conduct extensive experiments on three public datasets. Results show that mg2vec significantly outperforms a suite of state-of-the-art baselines in relationship mining tasks including relationship prediction, search and visualization.

Udwadia–Kalaba constraint-based tracking control for artificial swarm mechanical systems: dynamic approach

A novel swarm tracking control for artificial swarm mechanical systems consisting of multiple mechanical agents is proposed. In this paper, the agents could not only perform some biological swarm behaviors, such as the repulsion and attraction between agents, but also track the moving target or desired trajectory together. Based on the artificial potential functions, the kinematic modeling of each agent is constructed. The kinematic performance of the swarm system is analyzed, which includes convergence, tracking, aggregation and formation. Inspired by Udwadia–Kalaba constraints, the kinematic modeling of the swarm system is treated as servo constraints and formulated in the second-order form. With the second-order constraints, the explicit servo constraint forces are derived. In virtue of the constraint forces in the closed form, we creatively design a dynamic control for each agent which guarantees the controlled swarm system to obey the required motion. The proposed control scheme is proved by a series of theorems and illustrated by the simulation of multiple nonholonomic mobile robots.

Constraint-Based Control Design for Uncertain Underactuated Mechanical System: Leakage-Type Adaptation Mechanism

In this article, we are dedicated to coping with the control design for underactuated mechanical system (UMS) with system uncertainties, which is also subject to a set of servo constraints. For the nominal system without any initial condition deviations, this article provides a general model-based servo control with the idea of second-order constraints, which can be derived from both holonomic and nonholonomic ones. For the uncertain system, with the uncertainties being separated into matched portions and mismatched portions, this article provides an adaptive robust control scheme to guarantee the UMS to attain the deterministic performance on the basis of nominal control. The leakage-type adaptive law is to size up the unknown uncertainty bounds. The cart-pole system and the rotational-translational actuator system are used to verify the availability of the proposed adaptive robust control.

Bifurcation variations and motion-ruled-surface evolution of a novel Schatz linkage induced metamorphic mechanism

This paper presents a novel 7R metamorphic mechanism induced by Schatz linkage. The mechanism can realize the reconfigurable switch between two assembly configurations of Schatz linkage without disassembly and reassembly. The mechanism has four different motion branches and twelve bifurcation points. Two of these motion branches are two assembly configurations of Schatz linkage, and the others are two different single degree-of-freedom spatial 7R mechanisms. Bifurcation variations of the mechanism are presented by the configuration space, which is obtained by using the numerical approach of closed-loop equations. Then, twelve bifurcation points are identified by first- and second-order constraint equations. Moreover, motion ruled surfaces of the coupler link are generated, which proves that the mechanism has four motion branches and can switch from one assembly configuration of Schatz linkage to the other assembly configuration through another two motion branches.