scholarly journals Influence Of Membership Function’s Shape On Portfolio Optimization Results

2016 ◽  
Vol 6 (1) ◽  
pp. 45-54 ◽  
Author(s):  
Aleksandra Rutkowska
Keyword(s):  
Portfolio Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Selection Process ◽  
Sufficient Conditions ◽  
Credibility Measure ◽  
Risk Minimization ◽  
Different Shapes ◽  
Necessary And Sufficient ◽  
Mean Variance

Abstract Portfolio optimization, one of the most rapidly growing field of modern finance, is selection process, by which investor chooses the proportion of different securities and other assets to held. This paper studies the influence of membership function’s shape on the result of fuzzy portfolio optimization and focused on portfolio selection problem based on credibility measure. Four different shapes of the membership function are examined in the context of the most popular optimization problems: mean-variance, mean-semivariance, entropy minimization, value-at-risk minimization. The analysis takes into account both: the study of necessary and sufficient conditions for the existence of extremes, as well as the statistical inference about the differences based on simulation.

scholarly journals s-Goodness for Low-Rank Matrix Recovery

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Lingchen Kong ◽  
Levent Tunçel ◽  
Naihua Xiu
Keyword(s):  
Linear Transformation ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Nuclear Norm ◽  
Low Rank ◽  
Matrix Recovery ◽  
Rank Matrix ◽  
Necessary And Sufficient ◽  
Low Rank Matrix Recovery ◽  
Low Rank Matrix

Low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, and system identification and control. This class of optimization problems is generally𝒩𝒫hard. A popular approach replaces the rank function with the nuclear norm of the matrix variable. In this paper, we extend and characterize the concept ofs-goodness for a sensing matrix in sparse signal recovery (proposed by Juditsky and Nemirovski (Math Program, 2011)) to linear transformations in LMR. Using the two characteristics-goodness constants,γsandγ^s, of a linear transformation, we derive necessary and sufficient conditions for a linear transformation to bes-good. Moreover, we establish the equivalence ofs-goodness and the null space properties. Therefore,s-goodness is a necessary and sufficient condition for exacts-rank matrix recovery via the nuclear norm minimization.

Necessary and sufficient conditions for weak efficiency in non-smooth vectorial optimization problems

Optimization ◽  
2009 ◽  
Vol 58 (8) ◽  
pp. 981-993 ◽  
Author(s):  
Lucelina Batista dos Santos ◽  
Adilson J.V. Brandão ◽  
Rafaela Osuna-Gómez ◽  
Marko A. Rojas-Medar
Keyword(s):  
Optimization Problems ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weak Efficiency ◽  
Necessary And Sufficient

scholarly journals An Entropy-Based Approach to Portfolio Optimization

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 332 ◽  
Author(s):  
Peter Joseph Mercurio ◽  
Yuehua Wu ◽  
Hong Xie
Keyword(s):  
Objective Function ◽  
Portfolio Optimization ◽  
Historical Data ◽  
Optimization Problems ◽  
Improved Method ◽  
Financial Industry ◽  
New Family ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

This paper presents an improved method of applying entropy as a risk in portfolio optimization. A new family of portfolio optimization problems called the return-entropy portfolio optimization (REPO) is introduced that simplifies the computation of portfolio entropy using a combinatorial approach. REPO addresses five main practical concerns with the mean-variance portfolio optimization (MVPO). Pioneered by Harry Markowitz, MVPO revolutionized the financial industry as the first formal mathematical approach to risk-averse investing. REPO uses a mean-entropy objective function instead of the mean-variance objective function used in MVPO. REPO also simplifies the portfolio entropy calculation by utilizing combinatorial generating functions in the optimization objective function. REPO and MVPO were compared by emulating competing portfolios over historical data and REPO significantly outperformed MVPO in a strong majority of cases.

scholarly journals Error Bounds and Finite Termination for Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenling Zhao ◽  
Daojin Song ◽  
Bingzhuang Liu
Keyword(s):  
Constrained Optimization ◽  
Error Bound ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Merit Function ◽  
Global Error Bound ◽  
Constrained Optimization Problems ◽  
Nonconvex Constrained Optimization ◽  
Necessary And Sufficient

We present a global error bound for the projected gradient of nonconvex constrained optimization problems and a local error bound for the distance from a feasible solution to the optimal solution set of convex constrained optimization problems, by using the merit function involved in the sequential quadratic programming (SQP) method. For the solution sets (stationary points set andKKTpoints set) of nonconvex constrained optimization problems, we establish the definitions of generalized nondegeneration and generalized weak sharp minima. Based on the above, the necessary and sufficient conditions for a feasible solution of the nonconvex constrained optimization problems to terminate finitely at the two solutions are given, respectively. Accordingly, the results in this paper improve and popularize existing results known in the literature. Further, we utilize the global error bound for the projected gradient with the merit function being computed easily to describe these necessary and sufficient conditions.

NECESSARY AND SUFFICIENT CONDITIONS FOR DYNAMIC OPTIMIZATION

2014 ◽  
Vol 20 (3) ◽  
pp. 667-684 ◽  
Author(s):  
A. Kerem Coşar ◽  
Edward J. Green
Keyword(s):  
Optimization Problems ◽  
Infinite Horizon ◽  
Sufficient Conditions ◽  
Transversality Condition ◽  
Necessary And Sufficient Conditions ◽  
Infinite Horizon Optimization ◽  
Sufficient Conditions For Optimality ◽  
The Government ◽  
Duality Approach ◽  
Necessary And Sufficient

We characterize the necessary and sufficient conditions for optimality in discrete-time, infinite-horizon optimization problems with a state space of finite or infinite dimension. It is well known that the challenging task in this problem is to prove the necessity of the transversality condition. To do this, we follow a duality approach in an abstract linear space. Our proof resembles that of Kamihigashi (2003), but does not explicitly use results from real analysis. As an application, we formalize Sims's argument that the no-Ponzi constraint on the government budget follows from the necessity of the tranversality condition for optimal consumption.

scholarly journals Minimization of nonsmooth integral functionals

1992 ◽  
Vol 15 (4) ◽  
pp. 673-679
Author(s):  
Nikolaos S. Papageorgiou ◽  
Apostolos S. Papageorgiou
Keyword(s):  
Sobolev Spaces ◽  
Convex Analysis ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Integral Functionals ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dimensional State Space ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

In this paper we examine optimization problems involving multidimensional nonsmooth integral functionals defined on Sobolev spaces. We obtain necessary and sufficient conditions for optimality in convex, finite dimensional problems using techniques from convex analysis and in nonconvex, finite dimensional problems, using the subdifferential of Clarke. We also consider problems with infinite dimensional state space and we finally present two examples.

Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone

2018 ◽  
Vol 24 (1) ◽  
pp. 45-54
Author(s):  
Aleksandra Stasiak
Keyword(s):  
Partial Order ◽  
Optimization Problems ◽  
Sufficient Conditions ◽  
Polyhedral Cone ◽  
Directional Derivatives ◽  
Pareto Minima ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Derivatives Of

Abstract Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212–221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.

Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures

2020 ◽  
Author(s):  
Xin Chen ◽  
Daniel Zhuoyu Long ◽  
Jin Qi
Keyword(s):  
Operations Research ◽  
Parametric Optimization ◽  
Optimization Problems ◽  
Lattice Structure ◽  
Sufficient Conditions ◽  
Comparative Statics ◽  
Necessary And Sufficient Conditions ◽  
Objective Functions ◽  
New Concepts ◽  
Necessary And Sufficient

The concept of supermodularity has received considerable attention in economics and operations research. It is closely related to the concept of complementarity in economics and has also proved to be an important tool for deriving monotonic comparative statics in parametric optimization problems and game theory models. However, only certain sufficient conditions (e.g., lattice structure) are identified in the literature to preserve the supermodularity. In this article, new concepts of mostly sublattice and additive mostly sublattice are introduced. With these new concepts, necessary and sufficient conditions for the constraint structures are established so that supermodularity can be preserved under various assumptions about the objective functions. Furthermore, some classes of polyhedral sets that satisfy these concepts are identified, and the results are applied to assemble-to-order systems.

Optimality Conditions for Pareto-Optimal Solutions

2016 ◽  
Vol 685 ◽  
pp. 142-147
Author(s):  
Vladimir Gorbunov ◽  
Elena Sinyukova
Keyword(s):  
Multicriteria Optimization ◽  
Optimization Problem ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Sufficient Conditions ◽  
Optimal Solutions ◽  
Main Criterion ◽  
Linear Optimization Problems ◽  
Necessary And Sufficient

In this paper the authors describe necessary conditions of optimality for continuous multicriteria optimization problems. It is proved that the existence of effective solutions requires that the gradients of individual criteria were linearly dependent. The set of solutions is given by system of equations. It is shown that for finding necessary and sufficient conditions for multicriteria optimization problems, it is necessary to switch to the single-criterion optimization problem with the objective function, which is the convolution of individual criteria. These results are consistent with non-linear optimization problems with equality constraints. An example can be the study of optimal solutions obtained by the method of the main criterion for Pareto optimality.

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