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517.98

A.M. Вершик (1984)

Zapiski naucnych seminarov Leningradskogo

A geometric point of view on mean-variance models

Piotr Jaworski (2003)

Applicationes Mathematicae

This paper deals with the mathematics of the Markowitz theory of portfolio management. Let E and V be two homogeneous functions defined on ℝⁿ, the first linear, the other positive definite quadratic. Furthermore let Δ be a simplex contained in ℝⁿ (the set of admissible portfolios), for example Δ : x₁+ ... + xₙ = 1, x i 0 . Our goal is to investigate the properties of the restricted mappings (V,E):Δ → ℝ² (the so called Markowitz mappings) and to classify them. We introduce the notion of a generic model...

A Mixed Integer Quadratic Programming Model for the Low Autocorrelation Binary Sequence Problem

Kratica, Jozef (2012)

Serdica Journal of Computing

In this paper the low autocorrelation binary sequence problem (LABSP) is modeled as a mixed integer quadratic programming (MIQP) problem and proof of the model’s validity is given. Since the MIQP model is semidefinite, general optimization solvers can be used, and converge in a finite number of iterations. The experimental results show that IQP solvers, based on this MIQP formulation, are capable of optimally solving general/skew-symmetric LABSP instances of up to 30/51 elements in a moderate time....

A numerically stable least squares solution to the quadratic programming problem

E. Übi (2008)

Open Mathematics

The strictly convex quadratic programming problem is transformed to the least distance problem - finding the solution of minimum norm to the system of linear inequalities. This problem is equivalent to the linear least squares problem on the positive orthant. It is solved using orthogonal transformations, which are memorized as products. Like in the revised simplex method, an auxiliary matrix is used for computations. Compared to the modified-simplex type methods, the presented dual algorithm QPLS...

A Polynomial-time Interior-point Algorithm for Convex Quadratic Semidefinite Optimization

Y. Q. Bai, F. Y. Wang, X. W. Luo (2010)

RAIRO - Operations Research

In this paper we propose a primal-dual interior-point algorithm for convex quadratic semidefinite optimization problem. The search direction of algorithm is defined in terms of a matrix function and the iteration is generated by full-Newton step. Furthermore, we derive the iteration bound for the algorithm with small-update method, namely, O( n log n ε ), which is best-known bound so far.

A variational model for urban planning with traffic congestion

Guillaume Carlier, Filippo Santambrogio (2005)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

A variational model for urban planning with traffic congestion

Guillaume Carlier, Filippo Santambrogio (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We propose a variational model to describe the optimal distributions of residents and services in an urban area. The functional to be minimized involves an overall transportation cost taking into account congestion effects and two aditional terms which penalize concentration of residents and dispersion of services. We study regularity properties of the minimizers and treat in details some examples.

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