We present a new admissible pivot method for linear programming that works with a sequence of improving primal feasible interior points and dual feasible interior points. This method is a practicable variant of the short admissible pivot sequence algorithm, which was suggested by Fukuda and Terlaky. Here, we also show that this method can be modified to terminate in finite pivot steps. Finedly,...

Hopfield neural networks and interior point methods are used in an integrated way to solve linear optimization problems. The Hopfield network gives warm start for the primal–dual interior point methods, which can be way ahead in the path to optimality. The approaches were applied to a set of real world linear programming problems. The integrated approaches provide promising results, indicating ...

Linear optimization (LO) is the fundamental problem of mathematical optimization. It admits an enormous number of applications in economics, engineering, science and many other fields. The three most significant classes of algorithms for solving LO problems are: Pivot, Ellipsoid and Interior Point Methods. Because Ellipsoid Methods are not efficient in practice we will concentrate on the comput...

We present a primal-dual interior point method (IPM) for solving smooth convex optimization problems which arise during the placement of integrated circuits. The interior point method represents a substantial enhancement in flexibility verses other methods while having similar computational requirements. We illustrate that iterative solvers are efficient for calculation of search directions dur...

The convergence of the Tapia indicators for infeasible{interior{point methods for solving degenerate linear complementarity problems is investigated. A new estimate of the rate of convergence of the Tapia indicators for the indices where both primal and dual variables vanish in the solution is obtained, showing that Tapia indicators for these indices converge slower than for other indices. Use ...

In this paper, we develop an efficient homogeneous and self-dual interior-point method for the linear programs arising in economic model predictive control. To exploit structure in the optimization problems, the algorithm employs a highly specialized Riccati iteration procedure. Simulations show that in comparison to conventional interior-point methods, our solver is a) significantly faster per...

We show that a modiication of the combined Phase I-Phase II interior-point algorithm for linear programming, due to Anstreicher, de Ghellinck and Vial, Fra-ley, and Todd, terminates in O(p nL) iterations from a suitable initial (interior but infeasible) solution. The algorithm either detects infeasibility, or approaches feasibility and optimality simultaneously, or generates a feasible primal-d...

We argue that the fireball observed at RHIC is (the analog of) a dual black hole. In previous works, we have argued that the large s behaviour of the total QCD cross section is due to production of dual black holes, and that in the QCD effective field theory it corresponds to a nonlinear soliton of the pion field. Now we argue that the RHIC fireball is this soliton. We calculate the soliton (bl...

In this paper, we study polynomial-time interior-point algorithms in view of information geometry. We introduce an information geometric structure for a conic linear program based on a self-concordant barrier function. Riemannian metric is defined with the Hessian of the barrier function. We introduce two connections ∇ and ∇∗ which roughly corresponds to the primal and the dual problem. The dua...

Conic quadratic optimization is the problem of minimizing a linear function subject to the intersection of an affine set and the product of quadratic cones. The problem is a convex optimization problem and has numerous applications in engineering, economics, and other areas of science. Indeed, linear and convex quadratic optimization is a special case. Conic quadratic optimization problems can ...