System Of Linear Inequalities Research Articles

Robust and continuous metric subregularity for linear inequality systems

This paper introduces two new variational properties, robust and continuous metric subregularity, for finite linear inequality systems under data perturbations. The motivation of this study goes back to the seminal work by Dontchev, Lewis, and Rockafellar (2003) on the radius of metric regularity. In contrast to the metric regularity, the unstable continuity behavoir of the (always finite) metric subregularity modulus leads us to consider the aforementioned properties. After characterizing both of them, the radius of robust metric subregularity is computed and some insights on the radius of continuous metric subregularity are provided.

From Calmness to Hoffman Constants for Linear Semi-infinite Inequality Systems

In this paper we focus on different---global, semilocal, and local---versions of Hoffman-type inequalities expressed in a variational form. In a first stage our analysis is developed for generic multifunctions between metric spaces, and we finally deal with the feasible set mapping associated with linear semi-infinite inequality systems (finitely many variables and possibly infinitely many constraints) parameterized by their right-hand sides. The Hoffman modulus is shown to coincide with the Lipschitz upper semicontinuity modulus and the supremum of calmness moduli when confined to multifunctions with a convex graph and closed images in a reflexive Banach space, which is the case for our feasible set mapping. Moreover, for this particular multifunction a formula---involving only the system's left-hand side---of the global Hoffman constant is derived, providing a generalization to our semi-infinite context of finite counterparts developed in the literature. In the particular case of locally polyhedral systems, the paper also provides a point-based formula for the (semilocal) Hoffman modulus in terms of the calmness moduli at certain feasible points (extreme points when the nominal feasible set contains no lines), yielding a practically tractable expression for finite systems.

Peningkatan Hasil Belajar Siswa Kelas VII SMP Kristen Tounwawan Pada Materi Persamaan Dan Pertidaksamaan Linear Satu Variabel Dengan Menggunakan Model Pembelajaran Kooperatif Tipe STAD

This study aims to determine the improvement of student learning outcomes on the material of one-variable linear equation and inequalities system by applyning the cooperativ types STAD model. The subjects in the study were all eighth grade students of SMP Kristen Tounwawan with a total of 25 students. This research is a Classroom Action Research with the teacher acting as a teacher acting as a teacher and lasts for 3 cycles. Data was collected using tests and observations. The data analysis technique uses quantitative analysis and quantitative analysis. The results of the analysis showed that there was an increase in student learning outcomens from the first cycle, 20% (5 students) who achieved the KKM 60 to the second cycle 48% (12 students) who reachd the KKM 60 and the cycle, 100% (25 students) who reach KKM . From the results obtained, the coopeative learning model of the material of a two-variable linear equation system.

On Robust Global Error Bounds for a Class of Uncertain Piecewise Linear Inequality Systems

This paper is concerned with the radius of robust global error bounds for an uncertain piecewise linear inequality system where the uncertain data are assumed to be in polytope uncertain sets. We first present a dual characterization for robust global error bounds of this uncertain piecewise linear inequality system. Then, we establish upper and lower bounds for the radius of robust global error bounds of the system of uncertain piecewise linear inequalities in terms of the Minkowski function generalized by the polytope uncertain sets. Moreover, we also investigate robust global error bounds for this uncertain piecewise linear inequality system when the uncertain polytope sets are symmetric sets.

Roulette: A Diverse Family of Feasible Fault Attacks on Masked Kyber

At Indocrypt 2021, Hermelink, Pessl, and Pöppelmann presented a fault attack against Kyber in which a system of linear inequalities over the private key is generated and solved. The attack requires a laser and is, understandably, demonstrated with simulations—not actual equipment. We facilitate and diversify the attack in four ways, thereby admitting cheaper and more forgiving fault-injection setups. Firstly, the attack surface is enlarged: originally, the two input operands of the ciphertext comparison are covered, and we additionally cover re-encryption modules such as binomial sampling and butterflies in the last layer of the inverse numbertheoretic transform (INTT). This extra surface also allows an attacker to bypass the custom countermeasure that was proposed in the Indocrypt paper. Secondly, the fault model is relaxed: originally, precise bit flips are required, and we additionally support set-to-0 faults, random faults, arbitrary bit flips, and instruction skips. Thirdly, masking and blinding methods that randomize intermediate variables kindly help our attack, whereas the IndoCrypt attack is like most other fault attacks either hindered or unaltered by countermeasures against passive side-channel analysis (SCA). Randomization helps because we randomly fault intermediate prime-field elements until a desired set of values is hit. If these prime-field elements are represented on a circle, which is a common visualization, our attack is analogous to spinning a roulette wheel until the ball lands in a desired set of pockets. Hence, the nickname. Fourthly, we accelerate and improve the error tolerance of solving the system of linear inequalities: run times of roughly 100 minutes are reduced to roughly one minute, and inequality error rates of roughly 1% are relaxed to roughly 25%. Benefiting from the four advances above, we use a reasonably priced ChipWhisperer® board to break a masked implementation of Kyber running on an ARM Cortex-M4 through clock glitching.

Mathematical problem-solving ability: The impact of self-regulated learning on the system of linear inequalities in two variables

This research aims to analyze the mathematical problem-solving ability of students in terms of self-regulated learning. The method used in this research is the qualitative descriptive method. There are 4 indicators of problem-solving ability in this research, namely understanding the problem, formulating the problem, solving the problem, and re-examining the answers. The four indicators of problem-solving ability can be met by subjects who have a high self-regulated learning category. Subjects with medium self-regulated learning category were only able to fulfill 3 indicators of problem-solving ability. Meanwhile, subjects with low self-regulated learning were only able to fulfill 2 indicators of problem-solving ability. The results showed that the ability to solve problems with high categories was owned by subjects with high self-regulated learning.

Stability and Sensitivity of Uncertain Linear Programs

The present paper deals with uncertain linear optimization problems where the objective function coefficient vector belongs to a compact convex uncertainty set and the feasible set is described by a linear semi-infinite inequality system (finitely many variables and possibly infinitely many constrainsts), whose coefficients are also uncertain. Perturbations of both, the objective coefficient vector set and the constraint coefficient set, are measured by the Hausdorff metric. The paper is mainly concerned with analyzing the Lipschitz continuity of the optimal value function, as well as the lower and upper semicontinuity in the sense of Berge of the optimal set mapping. Inspired by Sion’s minimax theorem, a new concept of weak optimal solution set is introduced and analyzed.

Counting Vertices of Integral Polytopes Defined by Facets

We present a number of complexity results concerning the problem of counting vertices of an integral polytope defined by a system of linear inequalities. The focus is on polytopes with small integer vertices, particularly 0/1 polytopes and half-integral polytopes.

KESULITAN BERPIKIR REFLEKTIF MATEMATIS SISWA DALAM MENYELESAIKAN SOAL PROGRAM LINEAR DI SMA NEGERI 5 KOTA TERNATE

This study aims to describe the difficulties of students' mathematical reflective thinking in solving linear programming problems. This type of research is descriptive qualitative. Data collection techniques used are test instruments, interviews and documentation. Data analysis techniques in this study are data reduction, data exposure, data triangulation and conclusion drawing. The subjects of this study were students of class XI IPA 1 SMA Negeri 5 Ternate City, totaling 24 students, then representatives were selected based on the categories of mathematical ability, high, medium and low. The results showed that students with high mathematical ability had difficulty in reflective thinking, namely, 1) difficulties in connecting new knowledge with previous understanding, students needed accuracy in translating story questions into mathematical models, 2) difficulties in evaluating aspects of the completion process, students had difficulty remembering. return to function graph material to solve problems using the graph method. Students with moderate mathematical ability, 1) difficulty in connecting new knowledge with previous understanding, students need to be thorough in solving contextual problems, 2) difficulty in finding relationships and formulating solutions, students find it difficult to recall function graph material, difficult to shade the solution area, 3 ) difficulties in evaluating the aspect of the completion process, students find it difficult to prove the truth of the answers using the graphical method. Students with low mathematical ability, 1) difficulty in connecting new knowledge with previous understanding, students find it difficult to translate story questions into mathematical models, difficult to recall material on a two-variable linear inequality system, 2) difficulty in finding relationships and formulating solutions, students have difficulty find coordinate points, draw graphs, find intersection points, substitute corner points into objective functions. 3) difficulty in evaluating aspects of the completion process, students find it difficult to prove the truth of the answers obtained by the graphical method. The difficulties experienced by students in reflective thinking were caused by students not remembering the previous material related to linear programming, as well as students' difficulties in the dimensions of fact, concept and procedural knowledge.

Lipschitz upper semicontinuity in linear optimization via local directional convexity

This work is focussed on computing the Lipschitz upper semicontinuity modulus of the argmin mapping for canonically perturbed linear programs. The immediate antecedent can be traced out from Camacho J et al. [2022. From calmness to Hoffman constants for linear semi-infinite inequality systems. Available from: https://arxiv.org/pdf/2107.10000v2.pdf], devoted to the feasible set mapping. The aimed modulus is expressed in terms of a finite amount of calmness moduli, previously studied in the literature. Despite the parallelism in the results, the methodology followed in the current paper differs notably from Camacho J et al. [2022] as far as the graph of the argmin mapping is not convex; specifically, a new technique based on a certain type of local directional convexity is developed.

Control of a Discrete Dynamical System with Noise

For a discrete dynamical control system with noise, we consider the problem of retaining a phase point in a given family of sets at discrete instants of time. We analyze the case where the control vectogram is a polyhedron defined by a system of linear inequalities. We prove some properties of specific polyhedra satisfying the linearity condition, which allows us to obtain a condition of retention in the explicit form. Necessary and sufficient conditions for the possibility of retention are given. The results obtained are illustrated by an example.

4-VARIABLE BOOLEAN FUNCTIONS REPRESENTATIONS CLASSIFICATION IN THE FORM OF NONLINEARITY MINIMAL DEGREE SEPARATING SURFACES

In this paper, a classification study was carried out on the construction of 4-variable Boolean functions representations classification in the form of nonlinearity minimal degree separating surfaces. To construct these surfaces was used an adaptive ellipsoid algorithm based on the Khachiyan algorithm for solving systems of linear inequalities with integer coefficients. To define Boolean functions, we used its graphical representation on the projection of a four-dimensional cube. The classification study carried out was not limited only to the search for a separating surface of the minimum degree of nonlinearity. Additionally, the task was set to find the surface with the smallest number of non-zero nonlinear terms in accordance with a given lexicographic order. Based on the results of the study, a catalog of separating surfaces of the nonlinearity minimum degree with the smallest number of nonlinear terms for Boolean functions of 4 variables is constructed, and it is also determined that 15 classes of geometric equivalence functions have a minimum degree of nonlinearity of 1, 166 - degree 2, 40 - degree 3, and 1 function degree 4.

Penerapan Kombinasi Teori Belajar Pavlov dengan Teori Belajar Kognitif Untuk Meningkatkan Hasil Belajar Matematika pada Siswa SMA Negeri 1 Indra Makmur

The purpose of this research is to find out whether by applying the combination of Pavlov's x-learning theory with cognitive learning theory can improve students' mathematics learning outcomes on the subject of a two-variable linear inequality system discussion at SMA Negeri 1 Indra Makmu and to find out how active students are in the learning process. The population of this research is all class X Science1. Student improvement data obtained in the field is written in tabular form. The table shows a very good increase in learning outcomes, so it can be concluded that by using the application of a combination of Pavlovh's theory of learning with cognitive learning on the subject of a two-variable linear inequality system, there is an increase in learning outcomes in class X Science 1 at SMA Negeri 1 Indra Makmur

Optimal portfolio choice for higher-order risk averters

The effects of higher-order risk aversion on optimal cross-sectional portfolio choice are investigated using portfolio optimization with Stochastic Dominance constraints. Tractable sufficient conditions for higher-degree dominance are introduced that take the form of a system of linear inequalities. Existing studies of active equity industry rotation are extended from lower degrees to higher degrees of dominance. Fourth-degree dominance assumes that investors are ‘prudent’ and ‘temperate’ and therefore like skewness and dislike kurtosis. Using this dominance criterion leads to superior out-of-sample investment performance, by allowing for more concentration in recent winner industries which tend to show persistent positive abnormal returns and a favorable higher-order risk profile due to the industry-level price momentum effect.

Optimization of Invariant Ellipsoid Technique for Sparse Controllers Design

The paper deals with the method for the design of linear controllers with sparse state feedback matrices for control the plants under conditions of unknown and bounded disturbances. The importance of the sparsity property in feedback can be explained by two factors. First, by minimizing the columnar norm of the feedback matrix in the control it becomes pos- sible to use a minimum number of measuring devices. Secondly, by minimizing the row norm of the feedback matrix, the required number of executive (control) devices is minimized. Both properties, if they are achievable in the synthesis of the controller, reduce the cost of the system and improve the fault tolerance and quality of regulation by reducing the structural complexity. The search algorithm for sparse matrices is based on the method of invariant ellipsoids and is formulated as a solution to a system of linear matrix inequalities with additional constraints. A special set of optimization conditions is proposed which for a disturbed system minimizes overshoot and overshoots in transient processes of the disturbed closed- loop system simultaneously with minimizing errors in the steady state. The proposed method also assumes the possibility of minimizing both the row norm of the feedback matrix and the column one, while preserving the robustness properties, which makes it possible to solve the sparse control problem (a sparse control is understood as a linear controller with a sparse feedback matrix). The efficiency of the proposed control scheme is confirmed by the results of computer modeling and comparison with some existing ones.

Abstract executions of stochastic discrete event systems

Stochastic discrete event systems play a steadily increasing role in reliability engineering and beyond in systems engineering. Designing stochastic discrete event systems presents however well-known difficulties: models are hard to debug and to validate because of the existence of infinitely many possible executions, itself due to stochastic delays, which are possibly intertwined with deterministic ones. In this article, revisiting ideas introduced in the framework of model-checking of timed and hybrid systems, we show that it is possible to abstract the time in stochastic discrete event systems. More specifically, we show that schedules of transitions can be abstracted into systems of linear inequalities and that abstract and concrete executions are bisimilar. The result presented in this article represents thus a very important step forward in quality assurance of stochastic models of complex technical systems. We illustrate the potential of the proposed approach by means of AltaRica 3.0 models.

Switched Max-Plus Linear-Dual Inequalities: Application in Scheduling of Multi-Product Processing Networks

P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the max-plus algebra and its dual, the min-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operations, each corresponding to an LDI, according to an infinite sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the schedule is fixed and periodic. We show that SLDIs can model single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose an algorithm to compute minimum and maximum cycle times for these processes that improves the time complexity of other existing approaches.

Convergence conditions for continuous and discrete models of population dynamics

Some classes of continuous and discrete generalized Volterra models of population dynamics are considered. It is supposed that there are relationships of the type "symbiosis", "compensationism" or "neutralism" between any two species in a biological community. The objective of the work is to obtain conditions under which the investigated models possess the convergence property. This means that the studying system admits a bounded solution that is globally asimptotically stable. To determine the required conditions, the V. I. Zubov's approach and its discrete-time counterpart are used. Constructions of Lyapunov functions are proposed, and with the aid of these functions, the convergence problem for the considered models is reduced to the problem of the existence of positive solutions for some systems of linear algebraic inequalities. In the case where parameters of models are almost periodic functions, the fulfilment of the derived conditions implies that limiting bounded solutions are almost periodic, as well. An example is presented illustrating the obtained theoretical conclusions.

Relaxation schemes for the joint linear chance constraint based on probability inequalities

<p style='text-indent:20px;'>This paper is concerned with the joint chance constraint for a system of linear inequalities. We discuss computationally tractble relaxations of this constraint based on various probability inequalities, including Chebyshev inequality, Petrov exponential inequalities, and others. Under the linear decision rule and additional assumptions about first and second order moments of the random vector, we establish several upper bounds for a single chance constraint. This approach is then extended to handle the joint linear constraint. It is shown that the relaxed constraints are second-order cone representable. Numerical test results are presented and the problem of how to choose proper probability inequalities is discussed.</p>

Fault-tolerant control system for the formation of carbon products

The production of carbon products is largely resource- and energy-intensive. That is why increasing the efficiency of this production is an urgent scientific and practical task, especially in modern conditions of constant growth of energy costs. An effective way to solve this problem is to create a modern process control system, taking into account possible failures of system components. A method for the synthesis of a fault-tolerant control system for the cyclic formation of carbon products has been developed, which takes into account control errors that are caused by malfunctions of controllers under conditions of unknown disturbances. According to the cyclic nature of the technological process under consideration, a control method with iterative learning was used in the synthesis of the control system. This method considers cyclic processes based on a two-dimensional model (2D model). The proposed control algorithm ensures the convergence of the control process with the task both in time and in each work cycle in order to promote the required quality of control even in the event of unknown disturbances and errors in the performance of controllers. The synthesis of the control system is based on the solution of a system of linear matrix inequalities. Based on the combination of a control method with iterative learning and a control method that takes into account failures in controllers, a method of constructing a fault-tolerant control system for the cyclic formation of carbon products has been synthesized to ensure acceptable operation of the control object in abnormal conditions. The control system has been synthesized by solving a system of linear matrix inequalities with the MATLAB software. In the future, it is necessary to consider optimal settings of the proposed control system and examine its effectiveness in comparison with conventional fault-tolerant systems for non-cyclic processes.