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A comparative study on optimization methods for the constrained nonlinear programming problems.
A complementarity approach for solving Leontief substitution systems and (generalized) Markov decision processes
A computationally efficient stable dual-mode type nonlinear predictive control algorithm
A dual approach to solving linear inequalities by unconstrained quadratic optimization.
A dynamic system approach to quadratic programming problems with penalty method.
A geometric point of view on mean-variance models
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, . 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
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 New Genetic Representation for Quadratic Assignment Problem
A new heuristic for the quadratic assignment problem.
A nonlinear projection neural network for solving interval quadratic programming problems and its stability analysis.
A numerically stable least squares solution to the quadratic programming problem
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 algorithm for projecting a vector on the intersection of a hyperplane and
A Polynomial-time Interior-point Algorithm for Convex Quadratic Semidefinite Optimization
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( log ), which is best-known bound so far.
A Quadratic Approximation Method for Minimizing a Class of Quasidifferentiable Functions.
A quadratic programming algorithm for large and sparse problems
A sensitivity result for quadratic second-order cone programming and its application
In this paper, we present a sensitivity result for quadratic second-order cone programming under the weak form of second-order sufficient condition. Based on this result, we analyze the local convergence of an SQP-type method for nonlinear second-order cone programming. The subproblems of this method at each iteration are quadratic second-order cone programming problems. Compared with the local convergence analysis done before, we do not need the assumption that the Hessian matrix of the Lagrangian...
A variational model for urban planning with traffic congestion
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
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.
Adaptive constraint reduction for training support vector machines.