Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

Mencarelli, Luca; d'Ambrosio, Claudia

doi:10.1111/itor.12541

Cited by 21 publications

(11 citation statements)

References 150 publications

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“…We consider two large-scale Markowitz portfolio [6,7] instances where the objective is a scalarized version of risk minimization (using correlation rather than covariance for better scaling) and return maximization. The system Ax ≤ b encodes the portfolio constraints 0 ≤ x ≤ 1 (with −x ≤ 0 being part of the inequality constraints) and j x j ≤ 1, which imply x 2 ≤ 1.…”

Section: Two Large Portfolio Instancesmentioning

confidence: 99%

Random Projections for Quadratic Programs over a Euclidean Ball

Poirion

d'Ambrosio

et al. 2019

Integer Programming and Combinatorial Optimization

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Random projections are used as dimensional reduction techniques in many situations. They project a set of points in a high dimensional space to a lower dimensional one while approximately preserving all pairwise Euclidean distances. Usually, random projections are applied to numerical data. In this paper, however, we present a successful application of random projections to quadratic programming problems subject to polyhedral and a Euclidean ball constraint. We derive approximate feasibility and optimality results for the lower dimensional problem. We then show the practical usefulness of this idea on many random instances, as well as on two portfolio optimization instances with over 25M nonzeros in the (quadratic) risk term. This paper has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement n. 764759 "MINOA".

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Section: Two Large Portfolio Instancesmentioning

confidence: 99%

Random Projections for Quadratic Programs over a Euclidean Ball

Poirion

d'Ambrosio

et al. 2019

Integer Programming and Combinatorial Optimization

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“…This method is the latest in a series of exact algorithm proposals for variants of MIQPs with cardinality constraints, often focusing on portfolio optimization applications, that includes, in particular, [52,295,48,60,165,164,18,88,107]. A recent survey of models and exact methods for portfolio selection tasks, including cases with cardinality constraints, is provided by [250]; another fairly broad overview of MIQP with cardinality constraints can be found in [355]. A MIQP algorithm for the special case of feature selection (or sparse regression), 0 -cons( Ax − b 2 , k, R n ), was proposed in [45], including the aforementioned ways to compute tighter big-M bounds; some statistical properties of such sparse regression problems and relations to their regularized versions are discussed in, e.g., [348,298].…”

Section: Cardinality-constrained Optimizationmentioning

confidence: 99%

Cardinality Minimization, Constraints, and Regularization: A Survey

Tillmann¹,

Bienstock²,

Lodi³

et al. 2021

Preprint

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We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse application fields such as signal and image processing, portfolio selection, or machine learning. The paper discusses general-purpose modeling techniques and broadly applicable as well as problem-specific exact and heuristic solution approaches. While our perspective is that of mathematical optimization, a main goal of this work is to reach out to and build bridges between the different communities in which cardinality optimization problems are frequently encountered. In particular, we highlight that modern mixed-integer programming, which is often regarded as impractical due to commonly unsatisfactory behavior of black-box solvers applied to generic problem formulations, can in fact produce provably high-quality or even optimal solutions for cardinality optimization problems, even in large-scale real-world settings. Achieving such performance typically draws on the merits of problem-specific knowledge that may stem from different fields of application and, e.g., shed light on structural properties of a model or its solutions, or lead to the development of efficient heuristics; we also provide some illustrative examples.

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“…The variances of the latter are given as priors gamma distributions. 15 See, for example, Mencarelli and D'Ambrosio [2018] for a survey on mathematical programming approaches for the portfolio selection problem. of the demand model, while the associated shaded regions represent the variance of the prediction.…”

Section: B1 Mean-variance Optimization Problemmentioning

confidence: 99%

e4clim 1.0: The Energy for a Climate Integrated Model: Description and Application to Italy

et al. 2019

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We develop an open-source Python software integrating flexibility needs from Variable Renewable Energies (VREs) in the development of regional energy mixes. It provides a flexible and extensible tool to researchers/engineers, and for education/outreach. It aims at evaluating and optimizing energy deployment strategies with high shares of VRE; assessing the impact of new technologies and of climate variability; conducting sensitivity studies. Specifically, to limit the algorithm's complexity, we avoid solving a full-mix cost-minimization problem by taking the mean and variance of the renewable production-demand ratio as proxies to balance services. Second, observations of VRE technologies being typically too short or nonexistent, the hourly demand and production are estimated from climate time-series and fitted to available observations. We illustrate e4clim's potential with an optimal recommissioning-study of the 2015 Italian PV-wind mix testing different climatedata sources and strategies and assessing the impact of climate variability and the robustness of the results.

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Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

Cited by 21 publications

References 150 publications

Random Projections for Quadratic Programs over a Euclidean Ball

Random Projections for Quadratic Programs over a Euclidean Ball

Cardinality Minimization, Constraints, and Regularization: A Survey

e4clim 1.0: The Energy for a Climate Integrated Model: Description and Application to Italy

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