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Relevant bibliographies by topics / Mathematical optimization. Programming (Mathematics) Convex programming

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Academic literature on the topic 'Mathematical optimization. Programming (Mathematics) Convex programming'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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Journal articles on the topic "Mathematical optimization. Programming (Mathematics) Convex programming"

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Ceria, Sebastián, and João Soares. "Convex programming for disjunctive convex optimization." Mathematical Programming 86, no. 3 (December 1, 1999): 595–614. http://dx.doi.org/10.1007/s101070050106.

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Fu, J. Y., and Y. H. Wang. "Arcwise Connected Cone-Convex Functions and Mathematical Programming." Journal of Optimization Theory and Applications 118, no. 2 (August 2003): 339–52. http://dx.doi.org/10.1023/a:1025451422581.

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Lewis, Adrian S., and Michael L. Overton. "Eigenvalue optimization." Acta Numerica 5 (January 1996): 149–90. http://dx.doi.org/10.1017/s0962492900002646.

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Optimization problems involving eigenvalues arise in many different mathematical disciplines. This article is divided into two parts. Part I gives a historical account of the development of the field. We discuss various applications that have been especially influential, from structural analysis to combinatorial optimization, and we survey algorithmic developments, including the recent advance of interior-point methods for a specific problem class: semidefinite programming. In Part II we primarily address optimization of convex functions of eigenvalues of symmetric matrices subject to linear constraints. We derive a fairly complete mathematical theory, some of it classical and some of it new. Using the elegant language of conjugate duality theory, we highlight the parallels between the analysis of invariant matrix norms and weakly invariant convex matrix functions. We then restrict our attention further to linear and semidefinite programming, emphasizing the parallel duality theory and comparing primal-dual interior-point methods for the two problem classes. The final section presents some apparently new variational results about eigenvalues of nonsymmetric matrices, unifying known characterizations of the spectral abscissa (related to Lyapunov theory) and the spectral radius (as an infimum of matrix norms).

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Zhou, XueGang, and JiHui Yang. "Global Optimization for the Sum of Concave-Convex Ratios Problem." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/879739.

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This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

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Thuy, Le Quang, Nguyen Thi Bach Kim, and Nguyen Tuan Thien. "Generating Efficient Outcome Points for Convex Multiobjective Programming Problems and Its Application to Convex Multiplicative Programming." Journal of Applied Mathematics 2011 (2011): 1–21. http://dx.doi.org/10.1155/2011/464832.

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Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems.

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Xu, Z. K., and S. C. Fang. "Unconstrained convex programming approach to linear programming." Journal of Optimization Theory and Applications 86, no. 3 (September 1995): 745–52. http://dx.doi.org/10.1007/bf02192167.

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fang, S. C., and H. S. J. Tsao. "An unconstrained convex programming approach to solving convex quadratic programming problems." Optimization 27, no. 3 (January 1993): 235–43. http://dx.doi.org/10.1080/02331939308843884.

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Senchukov, Viktor. "The solution of optimization problems in the economy by overlaying integer lattices: applied aspect." Economics of Development 18, no. 1 (June 10, 2019): 44–55. http://dx.doi.org/10.21511/ed.18(1).2019.05.

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The results of generalization of scientific approaches to the solution of modern economic optimization tasks have shown the need for a new vision of their solution based on the improvement of existing mathematical tools. It is established that the peculiarities of the practical use of existing mathematical tools for solving economic optimization problems are caused by the problems of enterprise management in the presence of nonlinear processes in the economy, which also require consideration of the corresponding characteristics of nonlinear dynamic processes. The approach to solving the problem of integer (discrete) programming associated with the difficulties that arise when applying precise methods (methods of separation and combinatorial methods) is proposed, namely: a fractional Gomorrhic algorithm – for solving entirely integer problems (by gradual "narrowing" areas of admissible solutions of the problem under consideration); the method of branches and borders - which involves replacing the complete overview of all plans by their partial directional over. Illustrative examples of schemes of geometric programming, fractional-linear programming, nonlinear programming with a non-convex region, fractional-nonlinear programming with a non-convex domain, and research on the optimum model of Cobb-Douglas model are given. The advanced mathematical tools on the basis of the method of overlaying integer grids (OIG), which will solve problems of purely discrete, and not only integer optimization, as an individual case, are presented in the context of solving optimization tasks of an applied nature and are more effective at the expense of reducing the complexity and duration of their solving. It is proved that appropriate analytical support should be used as an economic and mathematical tool at the stage of solving tasks of an economic nature, in particular optimization of the parameters of the processes of organization and preparation of production of new products of the enterprises of the real sector of the economy.

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Trujillo-Cortez, R., and S. Zlobec. "Bilevel convex programming models." Optimization 58, no. 8 (November 2009): 1009–28. http://dx.doi.org/10.1080/02331930701763330.

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Gil-González, Walter, Oscar Danilo Montoya, Luis Fernando Grisales-Noreña, Fernando Cruz-Peragón, and Gerardo Alcalá. "Economic Dispatch of Renewable Generators and BESS in DC Microgrids Using Second-Order Cone Optimization." Energies 13, no. 7 (April 3, 2020): 1703. http://dx.doi.org/10.3390/en13071703.

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A convex mathematical model based on second-order cone programming (SOCP) for the optimal operation in direct current microgrids (DCMGs) with high-level penetration of renewable energies and battery energy storage systems (BESSs) is developed in this paper. The SOCP formulation allows converting the non-convex model of economic dispatch into a convex approach that guarantees the global optimum and has an easy implementation in specialized software, i.e., CVX. This conversion is accomplished by performing a mathematical relaxation to ensure the global optimum in DCMG. The SOCP model includes changeable energy purchase prices in the DCMG operation, which makes it in a suitable formulation to be implemented in real-time operation. An energy short-term forecasting model based on a receding horizon control (RHC) plus an artificial neural network (ANN) is used to forecast primary sources of renewable energy for periods of 0.5h. The proposed mathematical approach is compared to the non-convex model and semidefinite programming (SDP) in three simulation scenarios to validate its accuracy and efficiency.

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Dissertations / Theses on the topic "Mathematical optimization. Programming (Mathematics) Convex programming"

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Yang, Yi. "Sequential convex approximations of chance constrained programming /." View abstract or full-text, 2008. http://library.ust.hk/cgi/db/thesis.pl?IELM%202008%20YANG.

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Li, Xinxin. "Some operator splitting methods for convex optimization." HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/43.

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Many applications arising in various areas can be well modeled as convex optimization models with separable objective functions and linear coupling constraints. Such areas include signal processing, image processing, statistical learning, wireless networks, etc. If these well-structured convex models are treated as generic models and their separable structures are ignored in algorithmic design, then it is hard to eﬀectively exploit the favorable properties that the objective functions possibly have. Therefore, some operator splitting methods have regained much attention from diﬀerent areas for solving convex optimization models with separable structures in diﬀerent contexts. In this thesis, some new operator splitting methods are proposed for convex optimiza- tion models with separable structures. We ﬁrst propose combining the alternating direction method of multiplier with the logarithmic-quadratic proximal regulariza- tion for a separable monotone variational inequality with positive orthant constraints and propose a new operator splitting method. Then, we propose a proximal version of the strictly contractive Peaceman-Rachford splitting method, which was recently proposed for the convex minimization model with linear constraints and an objective function in form of the sum of two functions without coupled variables. After that, an operator splitting method suitable for parallel computation is proposed for a convex model whose objective function is the sum of three functions. For the new algorithms, we establish their convergence and estimate their convergence rates measured by the iteration complexity. We also apply the new algorithms to solve some applications arising in the image processing area; and report some preliminary numerical results. Last, we will discuss a particular video processing application and propose a series of new models for background extraction in diﬀerent scenarios; to which some of the new methods are applicable. Keywords: Convex optimization, Operator splitting method, Alternating direction method of multipliers, Peaceman-Rachford splitting method, Image processing

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Wright, Stephen E. "Convergence and approximation for primal-dual methods in large-scale optimization /." Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/5751.

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Zeng, Shangzhi. "Algorithm-tailored error bound conditions and the linear convergence rae of ADMM." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/474.

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In the literature, error bound conditions have been widely used for studying the linear convergence rates of various first-order algorithms and the majority of literature focuses on how to sufficiently ensure these error bound conditions, usually posing more assumptions on the model under discussion. In this thesis, we focus on the alternating direction method of multipliers (ADMM), and show that the known error bound conditions for studying ADMM's linear convergence, can indeed be further weakened if the error bound is studied over the specific iterative sequence generated by ADMM. A so-called partial error bound condition, which is tailored for the specific ADMM's iterative scheme and weaker than known error bound conditions in the literature, is thus proposed to derive the linear convergence of ADMM. We further show that this partial error bound condition theoretically justifies the difference if the two primal variables are updated in different orders in implementing ADMM, which had been empirically observed in the literature yet no theory is known so far.

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Theußl, Stefan, Florian Schwendinger, and Kurt Hornik. "ROI: An extensible R Optimization Infrastructure." WU Vienna University of Economics and Business, 2019. http://epub.wu.ac.at/5858/1/ROI_StatReport.pdf.

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Optimization plays an important role in many methods routinely used in statistics, machine learning and data science. Often, implementations of these methods rely on highly specialized optimization algorithms, designed to be only applicable within a specific application. However, in many instances recent advances, in particular in the field of convex optimization, make it possible to conveniently and straightforwardly use modern solvers instead with the advantage of enabling broader usage scenarios and thus promoting reusability. This paper introduces the R Optimization Infrastructure which provides an extensible infrastructure to model linear, quadratic, conic and general nonlinear optimization problems in a consistent way. Furthermore, the infrastructure administers many different solvers, reformulations, problem collections and functions to read and write optimization problems in various formats.
Series: Research Report Series / Department of Statistics and Mathematics

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Visagie, S. E. "Algoritmes vir die maksimering van konvekse en verwante knapsakprobleme /." Link to the online version, 2007. http://hdl.handle.net/10019.1/1082.

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Luedtke, James. "Integer Programming Approaches for Some Non-convex and Stochastic Optimization Problems." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19711.

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In this dissertation we study several non-convex and stochastic optimization problems. The common theme is the use of mixed-integer programming (MIP) techniques including valid inequalities and reformulation to solve these problems. We first study a strategic capacity planning model which captures the trade-off between the incentive to delay capacity installation to wait for improved technology and the need for some capacity to be installed to meet current demands. This problem is naturally formulated as a MIP with a bilinear objective. We develop several linear MIP formulations, along with classes of strong valid inequalities. We also present a specialized branch-and-cut algorithm to solve a compact concave formulation. Computational results indicate that these formulations can be used to solve large-scale instances. We next study methods for optimization with joint probabilistic constraints. These problems are challenging because evaluating solution feasibility requires multidimensional integration and the feasible region is not convex. We propose and analyze a Monte Carlo sampling scheme to simplify the probabilistic structure of such problems. Computational tests of the approach indicate that it can yield good feasible solutions and reasonable bounds on their quality. Next, we study a MIP formulation of the non-convex sample approximation problem. We obtain two strengthened formulations. As a byproduct of this analysis, we obtain new results for the previously studied mixing set, subject to an additional knapsack inequality. Computational results indicate that large-scale instances can be solved using the strengthened formulations. Finally, we study optimization problems with stochastic dominance constraints. A stochastic dominance constraint states that a random outcome which depends on the decision variables should stochastically dominate a given random variable. We present new formulations for both first and second order stochastic dominance which are significantly more compact than existing formulations. Computational tests illustrate the benefits of the new formulations.

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Dadush, Daniel Nicolas. "Integer programming, lattice algorithms, and deterministic volume estimation." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44807.

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The main subject of this thesis is the development of new geometric tools and techniques for solving classic problems within the geometry of numbers and convex geometry. At a high level, the problems considered in this thesis concern the varied interplay between the continuous and the discrete, an important theme within computer science and operations research. The first subject we consider is the study of cutting planes for non-linear integer programs. Cutting planes have been implemented to great effect for linear integer programs, and so understanding their properties in more general settings is an important subject of study. As our contribution to this area, we show that Chvatal-Gomory closure of any compact convex set is a rational polytope. As a consequence, we resolve an open problem of Schrijver (Ann. Disc. Math. `80) regarding the same question for irrational polytopes. The second subject of study is that of ellipsoidal approximation of convex bodies. Different such notions have been important to the development of fundamental geometric algorithms: e.g. the ellipsoid method for convex optimization (enclosing ellipsoids), or random walk methods for volume estimation (inertial ellipsoids). Here we consider the construction of an ellipsoid with good "covering" properties with respect to a convex body, known in convex geometry as the M-ellipsoid. As our contribution, we give two algorithms for constructing M-ellipsoids, and provide an application to near-optimal deterministic volume estimation in the oracle model. Equipped with this new geometric tool, we move to the study of classic lattice problems in the geometry of numbers, namely the Shortest (SVP) and Closest Vector Problems (CVP). Here we use M-ellipsoid coverings, combined with an algorithm of Micciancio and Voulgaris for CVP in the ℓ₂ norm (STOC `10), to obtain the first deterministic 2^O(ⁿ) time algorithm for the SVP in general norms. Combining this algorithm with a novel lattice sparsification technique, we derive the first deterministic 2^O(ⁿ)(1+1/ϵ)ⁿ time algorithm for (1+ϵ)-approximate CVP in general norms. For the next subject of study, we analyze the geometry of general integer programs. A central structural result in this area is Kinchine's flatness theorem, which states that every lattice free convex body has integer width bounded by a function of dimension. As our contribution, we build on the work Banaszczyk, using tools from lattice based cryptography, to give a new and tighter proof of the flatness theorem. Lastly, combining all the above techniques, we consider the study of algorithms for the Integer Programming Problem (IP). As our main contribution, we give a new 2^O(ⁿ)nⁿ time algorithm for IP, which yields the fastest currently known algorithm for IP and improves on the classic works of Lenstra (MOR `83) and Kannan (MOR `87).

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Potaptchik, Marina. "Portfolio Selection Under Nonsmooth Convex Transaction Costs." Thesis, University of Waterloo, 2006. http://hdl.handle.net/10012/2940.

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We consider a portfolio selection problem in the presence of transaction costs. Transaction costs on each asset are assumed to be a convex function of the amount sold or bought. This function can be nondifferentiable in a finite number of points. The objective function of this problem is a sum of a convex twice differentiable function and a separable convex nondifferentiable function. We first consider the problem in the presence of linear constraints and later generalize the results to the case when the constraints are given by the convex piece-wise linear functions.

Due to the special structure, this problem can be replaced by an equivalent differentiable problem in a higher dimension. It's main drawback is efficiency since the higher dimensional problem is computationally expensive to solve.

We propose several alternative ways to solve this problem which do not require introducing new variables or constraints. We derive the optimality conditions for this problem using subdifferentials. First, we generalize an active set method to this class of problems. We solve the problem by considering a sequence of equality constrained subproblems, each subproblem having a twice differentiable objective function. Information gathered at each step is used to construct the subproblem for the next step. We also show how the nonsmoothness can be handled efficiently by using spline approximations. The problem is then solved using a primal-dual interior-point method.

If a higher accuracy is needed, we do a crossover to an active set method. Our numerical tests show that we can solve large scale problems efficiently and accurately.

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Lan, Guanghui. "Convex optimization under inexact first-order information." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29732.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Arkadi Nemirovski; Committee Co-Chair: Alexander Shapiro; Committee Co-Chair: Renato D. C. Monteiro; Committee Member: Anatoli Jouditski; Committee Member: Shabbir Ahmed. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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Books on the topic "Mathematical optimization. Programming (Mathematics) Convex programming"

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Foundations of optimization. New York: Springer, 2010.

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Șandru, Ovidiu-Ilie. Noneuclidean convexity: Applications in the programming theory. București: Editura Tehnică, 1998.

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Rubinov, Aleksandr Moiseevich. Abstract convexity and global optimization. Dordrecht: Kluwer Academic Publishers, 2000.

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Joaquim António dos Santos Gromicho. Quasiconvex optimization and location theory. Dordrecht: Kluwer, 1997.

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Joaquim António dos Santos Gromicho. Quasiconvex optimization and location theory. Amsterdam: Thesis Publishers, 1995.

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Hiriart-Urruty, Jean-Baptiste. Fundamentals of convex analysis. Berlin: Springer, 2001.

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1944-, Lemaréchal Claude, ed. Fundamentals of convex analysis. Berlin: Springer, 2001.

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Convex analysis and global optimization. Dordrecht: Kluwer Academic Publishers, 1998.

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Xiaoqi, Yang, ed. Lagrange-type functions in constrained non-convex optimization. Boston: Kluwer Academic Publishers, 2003.

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Gao, David Yang. Duality principles in nonconvex systems: Theory, methods, and applications. Dordrecht: Kluwer Academic Publishers, 2000.

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Book chapters on the topic "Mathematical optimization. Programming (Mathematics) Convex programming"

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Auslender, Alfred. "Numerical methods for nondifferentiable convex optimization." In Mathematical Programming Studies, 102–26. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0121157.

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Eremeev, Anton V., Nikolay N. Tyunin, and Alexander S. Yurkov. "Non-Convex Quadratic Programming Problems in Short Wave Antenna Array Optimization." In Mathematical Optimization Theory and Operations Research, 34–45. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22629-9_3.

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Titov, Alexander A., Fedor S. Stonyakin, Mohammad S. Alkousa, Seydamet S. Ablaev, and Alexander V. Gasnikov. "Analogues of Switching Subgradient Schemes for Relatively Lipschitz-Continuous Convex Programming Problems." In Mathematical Optimization Theory and Operations Research, 133–49. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58657-7_13.

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Sonnevend, Gy. "New Algorithms in Convex Programming Based on a Notion of “Centre” (for Systems of Analytic Inequalities) and on Rational Extrapolation." In Trends in Mathematical Optimization, 311–26. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9297-1_20.

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Kotas, Jakob. "Mathematical Decision-Making with Linear and Convex Programming." In Foundations for Undergraduate Research in Mathematics, 171–91. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66065-3_8.

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Vagaská, Alena, and Miroslav Gombár. "Mathematical Optimization and Application of Nonlinear Programming." In Algorithms as a Basis of Modern Applied Mathematics, 461–86. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61334-1_24.

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Zionts, Stanley. "Multiple Criteria Mathematical Programming: An Overview and Several Approaches." In Mathematics of Multi Objective Optimization, 227–73. Vienna: Springer Vienna, 1985. http://dx.doi.org/10.1007/978-3-7091-2822-0_11.

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"3. Conic Programming and Duality." In A Mathematical View of Interior-Point Methods in Convex Optimization, 65–113. Society for Industrial and Applied Mathematics, 2001. http://dx.doi.org/10.1137/1.9780898718812.ch3.

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Sadeghi, Saeid, Maghsoud Amiri, and Farzaneh Mansoori Mooseloo. "Artificial Intelligence and Its Application in Optimization under Uncertainty." In Artificial Intelligence. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.98628.

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Nowadays, the increase in data acquisition and availability and complexity around optimization make it imperative to jointly use artificial intelligence (AI) and optimization for devising data-driven and intelligent decision support systems (DSS). A DSS can be successful if large amounts of interactive data proceed fast and robustly and extract useful information and knowledge to help decision-making. In this context, the data-driven approach has gained prominence due to its provision of insights for decision-making and easy implementation. The data-driven approach can discover various database patterns without relying on prior knowledge while also handling flexible objectives and multiple scenarios. This chapter reviews recent advances in data-driven optimization, highlighting the promise of data-driven optimization that integrates mathematical programming and machine learning (ML) for decision-making under uncertainty and identifies potential research opportunities. This chapter provides guidelines and implications for researchers, managers, and practitioners in operations research who want to advance their decision-making capabilities under uncertainty concerning data-driven optimization. Then, a comprehensive review and classification of the relevant publications on the data-driven stochastic program, data-driven robust optimization, and data-driven chance-constrained are presented. This chapter also identifies fertile avenues for future research that focus on deep-data-driven optimization, deep data-driven models, as well as online learning-based data-driven optimization. Perspectives on reinforcement learning (RL)-based data-driven optimization and deep RL for solving NP-hard problems are discussed. We investigate the application of data-driven optimization in different case studies to demonstrate improvements in operational performance over conventional optimization methodology. Finally, some managerial implications and some future directions are provided.

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"10. Optimization (Including Linear; Nonlinear, Dynamic, and Geometric Programming, Control Theory, Games and Other Miscellaneous Topics)." In Mathematical Modelling: Classroom Notes in Applied Mathematics, 226–51. Society for Industrial and Applied Mathematics, 1987. http://dx.doi.org/10.1137/1.9781611971767.ch10.

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Conference papers on the topic "Mathematical optimization. Programming (Mathematics) Convex programming"

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Jiang, Tao, and Mehran Chirehdast. "A Systems Approach to Structural Topology Optimization: Designing Optimal Connections." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/dac-1474.

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Abstract In this paper, structural topology optimization is extended to systems design. Locations and patterns of connections in a structural system that consists of multiple components strongly affect its performance. Topology of connections is defined, and a new classification for structural optimization is introduced that includes the topology optimization problem for connections. A mathematical programming problem is formulated that addresses this design problem. A convex approximation method using analytical gradients is used to solve the optimization problem. This solution method is readily applicable to large-scale problems. The design problem presented and solved here has a wide range of applications in all areas of structural design. The examples provided here are for spot-weld and adhesive bond joints. Numerous other potential applications are suggested.

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Mathelinea, Devy, R. Chandrashekar, and Nur Farah Adilah Che Omar. "Inventory cost optimization through nonlinear programming with constraint and forecasting techniques." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH2018): Innovative Technologies for Mathematics & Mathematics for Technological Innovation. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5136384.

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Shafat, Gabriel, Binyamin Abramov, and Ilya Levin. "Using Threshold Functions in Teaching Electronics." In ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2008. http://dx.doi.org/10.1115/esda2008-59125.

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Teaching of digital electronics and the teaching of analog electronics differ significantly. The methods in use today differ in two major points: the required mathematical background and the used didactic methods. The well-known gap between the analog and the digital paradigms in teaching electronics has motivated the present study. The paper introduces a novel approach for electronics course teaching. The approach uses a concept threshold functions. Threshold functions have three remarkable properties that are suitable for the purposes of teaching an electronics course. The first property is the simplicity of the functions’ representation and implementation; the essence of a threshold function is understandable on the common sense level. The second property is the dual analog-digital nature of the threshold functions. The definition of a threshold function usually includes both Boolean and arithmetic portions and weaves together the two alternative domains: digital and analog. Since students are familiar with regular arithmetic functions from previous math courses, the addition of Boolean concepts is simple to grasp. The possibility to transform any threshold function from one domain to another, serves as a powerful tool for processes teaching. The third property we consider is the multiple representations possible for threshold functions. Besides the classical Boolean and arithmetic representations, a threshold function can be represented in the format of an electric/electronic circuit and also can be represented in a spatial form, by three-dimensional visualization for better understanding the functional properties of threshold functions. The paper discusses a problem-based learning with two main types of problems: synthesis and analysis problems of threshold elements. While the analysis problem is relatively simple, the problem of optimal synthesis is NP-complete, and equivalent to a well-known optimization problem that exists also in linear programming. Using the linear programming for teaching the synthesis of a threshold element is a challenging pedagogical task. The paper describes an approach for solving this task. A number of real-world problems may be formulated and efficiently solved by using the proposed threshold-based approach, for example the problems of event-driven control, fuzzy control, linear optimization, self-regulation. These problems formulate as students’ assignments, and are used in the lesson. These exercises convert a lesson of electronics into an interesting, challengeable and useful educational event. Introduction of the threshold approach into the electronics curriculum enables the students to acquire much deeper understanding of electronic systems.

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