Iderbayar Shiilegbat, Rentsen Enkhbat · Journal of Institute of Mathematics and Digital Technology · 2023
In 1803 Italian mathematician Malfatti posed the following problem how to pack three non-overlapping circles of maximum total area in a given triangle. Malfatti originally assumed that the solution to this problem are three circles inscribed in a triangle such that each circle tangent to other two and touches two sides of the triangle. Now it is well known that Malfatti’s solution is not optimal. The problem for the first time was treated as a global optimization problem in Enkhbat [9]. In this paper, we consider a new formulation of Malfatti’s problem called Malfatti’s constrained optimization problem. The new problem is formulated as a nonconvex optimization problem with nonlinear constraints. Numerical experiments were conducted on Python for the cases. Мальфаттын зааглалтай бодлого Хураангуй: 1803 онд анх Италийн математикч Мальфатт өгөгдсөн гурвалжинд хамгийн их талбайтай, давхцахгүйгээр гурван тойргийг хэрхэн байрлуулах вэ? гэсэн бодлогыг тавьж байсан бөгөөд энэхүү бодлогын шийд нь гурвалжинд багтсан гурван тойргуудын тойрог бүр нөгөө хоёр тойргийг, гурвалжны хоёр талыг шүргэсэн байна гэж үзсэн.Энэ нь хараахан оновчтой шийд биш байсан ба [9] ажилд анх Мальфаттын бодлогыг бодох глобал оновчлолын бодлогыг томьёолж шийдийг олох арга алгоритм боловсруулсан. Энэхүү судалгаанд бид Мальфаттын бодлогын шинэ томьёолол буюу Хөдөлгөөнт Мальфаттын бодлогыг авч үзсэн. Тус бодлого нь шугаман бус хязгаарлалттай гүдгэр бус оновчлолын бодлого юм. Тоон туршилтыг Python дээр хийсэн. Түлхүүр үгс: Мальфаттын бодлого, гүдгэр бус оновчлол, тойрог, гурвалжин
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Sherry May · Journal of Philosophical Logic · 1976
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V I George, Ciji Pearl Kurian · 2002
This paper concerns with designing a controller (compensator) in frequency domain. A set of basic frequency domain performance requirements are presented and it has a convenient graphical interpretation in terms of disks. We state a problem of optimizing a performance function defined in terms of weighted sensitivity function S over the closed loop transfer function T that satisfies the closed loop constraint for a feedback system. The idea of Barrier (Penalty) function method is used for optimizing the above constrained optimization problem in to an unconstrained minimization problem, optimize a performance function and obtain an optimal designable transfer function T and derives a rational compensator C. Any high performance technical computing languages are used for solving the optimization problem.
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Keivan Shariatmadar, Erik Quaeghebeur, Gert de Cooman · Lirias (KU Leuven) · 2009
Consider the following optimization problem: maximize a bounded real-valued function f -defined on a set X -over all x in X that satisfy the constraint xRY , where Y is a random variable taking values in a set Y and R is a relation on X Y .The aim of our active research is to reduce this problem to a (constrained) optimization problem from which the uncertainties present in the description of the constraint are eliminated.We investigate what results can be obtained for different types of uncertainty models for the random variable Y -linear previsions, vacuous previsions, possibility distributions, p-boxes, etc. [see, e.g., 1, 2, 4] -and for two different optimality criteria -maximinity and maximality [see, e.g., 3].We work with general X , Y , and R for the combinations of uncertainty model and optimality criterion that allow it and restrict our attention to more concrete situations otherwise.
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Leclerc, Matthias, Rendl, Franz · Computer Science Publication Server (University of Cologne) · 1989
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Xianping Guo, Qingda Wei, Junyu Zhang · Birkhäuser Boston eBooks · 2012
First, we introduce a constrained optimization problem in which the objective function is defined on the product space of a linear space and a convex set. The goal of this optimization problem is to maximize values of the function with any fixed variable in the linear space, over the subset of the convex set given by the function with another fixed variable from the linear space and with a constraint. We give suitable conditions under which the existence of a constrained-optimal solution to the optimization problem is shown. Then, we apply the main results obtained here to the existing discrete- and continuous-time constrained Markov decision processes (MDPs) with the discounted and average criteria, and also establish the existence of constrained-optimal policies and characterize a constrained-optimal policy without the nonnegativity assumption on the costs as in the previous literature. Furthermore, we apply our results to discrete-time constrained MDPs with state-dependent discount factors.
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H. Hauptman · 1998
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Zhuangzhi Li, Zukui Li, Zukui Li et al. · Computers & Chemical Engineering · 2015
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Van Chien Le, Thi Thanh Mai Ta · Computational and Applied Mathematics · 2021
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Cor J. Veenman, Marcel Reinders, E. Backer · Pattern Recognition · 2003
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Yishou Wang, Yanjun Shi, Hong‐Fei Teng · 2007
We explore the meta-heuristic approach called scatter search for the constrained layout optimization. The scatter search framework is flexible and allows the development of alternative implementations for different problems. We empirically study the coordinate transformation-based diversification method and the reference set update method on the basis of two dissimilarities. We present two approaches using a scatter search framework. One only uses the gradient descent algorithm as the improvement method, so-called basic scatter search. The other, so- called hybrid scatter search, adopts gradient descent and Nelder-Mead simplex algorithm to improve the trial solution generated at two different stages. We attempt to determine the efficiency and efficacy of two variants of scatter search. Case studies show that the experimental results are either superior or comparable to the best known published results. The results also show that the hybrid scatter search is better than the basic scatter search for the constrained layout optimization problems.
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Harro Walk · Communications in Statistics Part C Sequential Analysis · 1983
A primal dual method of Kushner and Sanvicente for a constrained optimization problem with convex regression functions is investigated without a priori bounds. For the stochastic approximation sequence almost sure convergence to a random optimal solution and a random Kuhn-Tucker vector is shown, and for the uniqueness case, a functional central limit theorem is given.
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2008
of test examples for nonlinear semidefinite programs, control system design and related problems F. LEIBFRITZ ∗ Abstract. The purpose of this paper is to describe a collection of test examples which can be used for testing and comparing algorithms for nonlinear semidefinite programs (NSDPs), bilinear matrix inequality (BMI) problems, (linear) control system design and related problems. COMPleib consists of examples collected from the engineering literature and real–life sources for linear time–invariant (LTI) control systems. It contains models from real world engineering applications as well as idealized or pure academic versions of problems similar to those arising in practice. This collection may serve directly for test purposes in the construction of new tools for LTI control system design, i. e. algorithms for model reduction, Riccati (Lyapunov) equation solvers, tools for H∞, H2 or mixed H2/H∞ controller synthesis. On the other hand, it is well–known, that a very wide variety of control synthesis problems can be reformulated as constrained matrix optimization problems. In example, the design of a low–order output feedback controller for a LTI system is an important instance of a difficult and in general non–convex, nonlinear control problem which can be transformed into a (non–convex) nonlinear semidefinite program. We present NSPD as well as BMI formulations of
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Qitong Pan, Yu Lin, Jiaying Wu et al. · Applied Mathematics in Science and Engineering · 2025
Mitigating portfolio risk and enhancing performance are key goals in portfolio optimization. Investors prioritize the long-term implications of wealth accumulation and the benchmark strategies employed to mitigate risk. This paper presents a multi-period mean-variance model which includes intertemporal constraints and tracking-error terms. We systematically tackle the multi-period mean-variance optimization problem, integrating these constraints and considerations. By employing dynamic programming and the Linear Quadratic control framework, we derive the optimal policy for our model. Using a numerical example, we show that the dynamic mean-variance model effectively increases returns while reducing variance and partial risk. This model helps investors maintain wealth stability, lower the chance of significant losses, and enhance risky returns during the investment period.
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Romain Duboscq, Olivier Pinaud · Journal of Functional Analysis · 2021
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Ben Salem, Mariem, Taktak, Raouia, Mahjoub, Ali Ridha et al. · Base Institutionnelle de Recherche de l'université Paris-Dauphine (BIRD) (University Paris-Dauphine) · 2018
This paper deals with the Knapsack Problem with conflicts, also known as the Disjunctively Constrained Knapsack Problem. The conflicts are represented by a graph whose vertices are the items such that adjacent items cannot be packed in the knapsack simultaneously. We consider a classical formulation for the problem, study the polytope associated with this formulation and investigate the facial aspect of its basic constraints. We then present new families of valid inequalities and describe necessary and sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities. Using these results, we develop a Branch-and-Cut algorithm for the problem. An extensive computational study is also presented.
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Strad Research · 2021
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Alhaji Shehu Grema, Yi Cao, Modu Bako Grema · Ife Journal of Science · 2018
Self-optimizing control (SOC) is a technique used in selecting controlled variables (CVs) for a process plant control structure with a view to operating the plant optimally in the presence of uncertainties and disturbances. Existing SOC approaches are either local which result to large losses or too cumbersome to be applicable to real systems. In this work, a novel method of CV selection based on data was developed. In the method, a compressed reduced gradient of a constrained optimization problem was proposed to be estimated using finite difference scheme. The CV function was then used to approximate the necessary condition of optimality (NCO) using data only in a single regression step. The new approach was applied to a simplified case study and its performance was compared to an existing SOC methodology. An excellent goodness of fit was obtained during the regression with a R2-value of 1.0 associated with one of the designed CVs. The formulated CVs were found to be very robust with performance similar to that of NCO approximation method. A zero loss was incurred with one of the CVs.Keywords: compressed reduced gradient, constrained problems, controlled variable, data-driven, necessary condition of optimality, self-optimizing control
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Laurent Autrique, J.P. Leyris, Eduardo Souza de Cursi · IFAC Proceedings Volumes · 1999
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Technische Universitat Graz, Medizinische Universitat Graz, Spezialforschungsbereich F et al. · 2011
Shape optimization problems in fluid dynamics governed by the free surface flows are considered. Such problems are inspired by the process of continuous casting of steel where optimization of large vortex structures in different metal-lurgical reactors is of paramount importance to ensure good quality output. The pseudo-transient approach is used as solution strategy for solving the free surface problem. Design sensitivities involving different cost functionals are derived using a formal Lagrangian framework. Numerical results are presented which indicate the success of the proposed algorithm for solving this free surface shape optimiza-tion problem.
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