Interior point methods (IPM) with direct solution of the underlying linear systems of equations have been used successfully to solve very large scale linear programming (LP) problems. However, the limitations of direct methods for some classes of problems have led to iterative techniques being considered. The matrix-free method is one such approach and is so named since the iterative solution p...

In this paper, we develop an interior-point method for solving a class of convex optimization problems with timevarying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system for tracking the (time-varying) optimal solution with an asymptotically vanishing error. This dynamical system is composed of two terms: (i) a correction term...

We consider a class of optimization problems for sparse signal reconstruction which arise in the field of Compressed Sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC AS, SPGL1, NestA, `1 `s, PDCO to mention a few. CS applications lead to very well conditioned optimization problems and therefore can be solved easily by simple first-order methods. ...

In this paper, we propose a primal interior-point method for large sparse minimax optimization. After a short introduction, the complete algorithm is introduced and important implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Thus the large sparse nonconvex minimax optimization problems can be solved successfully. The results o...

Mathematical program with equilibrium constraints (MPEC) has extensive applications in practical areas such as traffic control, engineering design, and economic modeling. Some generalized stationary points of MPEC are studied to better describe the limiting points produced by interior point methods for MPEC. A primal-dual interior point method is then proposed, which solves a sequence of relaxe...

In predictive control, a quadratic program (QP) needs to be solved at each sampling instant. We present a new warm-start strategy to solve a QP with an interior-point method whose data is slightly perturbed from the previous QP. In this strategy, an initial guess of the unknown variables in the perturbed problem is determined from the computed solution of the previous problem. We demonstrate th...

In multicriteria optimization, several objective functions, conflicting with each other, have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multiobjective programming problem, where the objective functions involved are arbitary convex functions and the set of feasible points is convex. The method is based on generating warm-start point...

Entropy optimization is used in signal compression, coding, estimation, and resource scheduling, among other applications. The paper presents a novel algorithm for entropy optimization. The algorithm is motivated by the efficient interior-point methods developed in Linear Programming. The algorithm uses a Generalized Affine Scaling Transformation that is an extension of the Affine Scaling Trans...

Si riportano i risultati ottenuti utilizzando un metodo del punto interno combinato con l’algoritmo dei gradienti coniugati precondizionati per la risoluzione di alcune applicazioni di grandi dimensioni su Cray T3E ed SGI Origin 2000. La prima applicazione riguarda problemi di programmazione stocastica e di ottimizzazione robusta, mentre la seconda deriva dalla riformulazione di una speciale cl...

In this paper we treat numerical computation methods for linear programming. Started from the analysis of the efficiency and defficiency of the simplex procedure, we present new possibilities offered by the interior-point methods, which appears from practical necessity, from the need of efficient means of solving large-scale problems. We realise the implementation in Java of the Karmarkar’s met...