The aim of this paper is to provide a detailed insight into two mathematical models,one linear and one non-linear,that tackles the asset allocation optimization *** have collected data for seven different investment o...
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The aim of this paper is to provide a detailed insight into two mathematical models,one linear and one non-linear,that tackles the asset allocation optimization *** have collected data for seven different investment options in the last *** data are then analyzed with python,including visualizing them with several different graphs and computing their covariance and *** models are solved by python as well,admitting two different asset allocation plans according to application scenarios.
Guides in the application of linear programming to firm decision making, with the goal of giving decision-makers a better understanding of methods at their disposal Useful as a main resource or as a supplement in an e...
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ISBN:
(数字)9781119509455
ISBN:
(纸本)9781119509448
Guides in the application of linear programming to firm decision making, with the goal of giving decision-makers a better understanding of methods at their disposal Useful as a main resource or as a supplement in an economics or management science course, this comprehensive book addresses the deficiencies of other texts when it comes to covering linear programming theory--especially where data envelopment analysis (DEA) is concerned--and provides the foundation for the development of DEA. linear programming and Resource Allocation Modeling begins by introducing primal and dual problems via an optimum product mix problem, and reviews the rudiments of vector and matrix operations. It then goes on to cover: the canonical and standard forms of a linear programming problem; the computational aspects of linear programming; variations of the standard simplex theme; duality theory; single- and multiple- process production functions; sensitivity analysis of the optimal solution; structural changes; and parametric programming. The primal and dual problems are then reformulated and re-examined in the context of Lagrangian saddle points, and a host of duality and complementary slackness theorems are offered. The book also covers primal and dual quadratic programs, the complementary pivot method, primal and dual linear fractional functional programs, and (matrix) game theory solutions via linear programming, and data envelopment analysis (DEA). This book: Appeals to those wishing to solve linear optimization problems in areas such as economics, business administration and management, agriculture and energy, strategic planning, public decision making, and health care Fills the need for a linear programming applications component in a management science or economics course Provides a complete treatment of linear programming as applied to activity selection and usage Contains many detailed example problems as well as textual and graphical explanations linear programming and Resourc
Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practic...
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A linear programming based framework is presented to derive finite blocklength converses for coding problems in information theory which is also extendable to network settings. In the point-to-point setting, the LP ba...
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ISBN:
(纸本)9781728101248
A linear programming based framework is presented to derive finite blocklength converses for coding problems in information theory which is also extendable to network settings. In the point-to-point setting, the LP based framework recovers and in fact improves on almost all well-known finite blocklength converses for lossy joint source-channel coding, lossy source coding and channel coding. Moreover, the LP based framework is shown to be asymptotically tight for the averaged and compound channels under the maximum probability of error criterion. Further, for multiterminal Slepian-Wolf source coding problem, a systematic approach to synthesize new converses from considering point-to-point lossless source coding (with side-information at decoder) sub-problems is introduced. The method derives new finite blocklength converse for Slepian-Wolf coding which significantly improves on the converse of Miyake and Kanaya.
The Lovász theta number is a semidefinite programming bound on the clique number of (the complement of) a given graph. Given a vertex-transitive graph, every vertex belongs to a maximal clique, and so one can ins...
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A numerical technique for stochastic control problems featuring singular control is derived. In these problems, the control is given by positioning a reflecting boundary in the state space of a given stochastic proces...
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ISBN:
(纸本)9781538654286
A numerical technique for stochastic control problems featuring singular control is derived. In these problems, the control is given by positioning a reflecting boundary in the state space of a given stochastic process. The position of the reflecting boundary has to be adjusted to maximize a given optimality criterion. The presented numerical technique uses a novel discretization approach to a linear programming framework for the occupation measures of the process. However, a non-linear solver has to be used to find the optimal position of the boundary. Proofs of the existence and uniqueness of solutions to the underlying linear constraints are outlined. The discretization of these constraints is conducted by a finite element type approach using finite dimensional subspaces, in order to find computable approximations. A convergence analysis for this approach is given. The technique is illustrated with an example from stochastic optimal harvesting.
Motivated by applications of rental services in e-commerce, we consider real-time assortment of reusable products. In our model, arriving consumers with heterogeneous types choose rental products from the offered asso...
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Motivated by applications of rental services in e-commerce, we consider real-time assortment of reusable products. In our model, arriving consumers with heterogeneous types choose rental products from the offered assortment, pay the rental fees, and return the product to the platform after a rental time. Consumers' types specify their choice models, rental fees and rental time distributions for various products. Our goal is to design competitive online policies against an appropriate benchmark for both the prior-free setting, in which types are arbitrary (or adversarial), and the Bayesian setting, in which types are drawn independently from known distributions. Our contribution is threefold. We first introduce offline linear programming benchmarks in both settings, that use time-varying inventory constraints to capture feasibility of a policy under rentals, and are required to satisfy these constraints only in expectation. Second, in the prior-free setting, we develop a randomized primal-dual framework based on our introduced LP to settle that inventory balancing policies of Golrezaei et al. (2014) obtain same (asymptotically optimal) competitive ratios as with non-reusable resources when product rental times are fixed over time. As a corollary, we obtain the optimal competitive ratio of (1 − 1/e) when inventories are large. We also show this family of policies are constant competitive under i.i.d. (over time) stochastic rental times. Third, we change gear to the Bayesian setting by introducing simulation-based policies that use the expected LP solution as guidance. By using primal-dual analysis, we obtain a (1/2)-competitive simple and static simulation-based policy against the expected LP for general type-varying rental time distributions and rental fees. We further show optimal (1 − 1/ (cmin+3)0.5)-competitive adaptive policies against the same benchmark when rental times are infinite, where cmin is the smallest product inventory. Our analysis extends tools in th
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that ...
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linear programming has the capability to optimize multilevel maintenance operations. Although addressed in maintainability documentation and papers for over 50 years, it is still not a commonly used tool. With the adv...
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ISBN:
(纸本)9781538628690
linear programming has the capability to optimize multilevel maintenance operations. Although addressed in maintainability documentation and papers for over 50 years, it is still not a commonly used tool. With the advent of Simplex Method Solvers in Excel, solutions to linear programming scenarios have become low cost and easily available. By addressing scenarios through identifying the primary goal and the constraints to the operations, linear programming is a highly useful tool for maintainability engineering and needs to be used on a more regular basis.
In coding theory, it is important to find upper bounds for the code size given a code length and minimum distance. The Hamming bounds and linear programming (LP) bounds were proposed in previous works. On the other ha...
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ISBN:
(纸本)9781538666500
In coding theory, it is important to find upper bounds for the code size given a code length and minimum distance. The Hamming bounds and linear programming (LP) bounds were proposed in previous works. On the other hand, Masnick et al. proposed Unequal Error Protection (UEP) codes and modified Hamming bounds as upper bounds for the code size of UEP codes. In our previous work, we defined 2-level UEP codes as a subclass of UEP codes, and derived LP bounds for 2-level UEP codes. In this paper, we define multi-level UEP codes by extending 2-level UEP codes, and derive LP bounds for multi-level UEP codes. Moreover, we show that LP bounds for UEP codes are tighter upper bound than modified Hamming bounds.
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