This paper proposes three numerical algorithms based on Karmarkar’s interior point technique for solving nonlinear convex programming problems subject to linear constraints. The first algorithm uses the Karmarkar idea and linearization of the objective function.The second and third algorithms are modification of the first algorithm using the Schrijver andMalek-Naseri approaches, respectively. T...

In this contribution we present two interior-point path-following algorithms that solve the convex optimisation problem that arises in recentred barrier function model predictive control (MPC), which includes standard MPC as a limiting case. However the optimisation problem that arises in nonlinear MPC may not be convex. In this case we propose sequential convex programming (SCP) as an alternat...

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In this paper we consider the question of solving equilibrium problems—formulated as complementarity problems and, more generally, mathematical programs with equilibrium constraints (MPEC’s)—as nonlinear programs, using an interior-point approach. These problems pose theoretical difficulties for nonlinear solvers, including interior-point methods. We examine the use of penalty methods to get ar...

An approach to determine primal and dual stepsizes in the infeasible{ interior{point primal{dual method for convex quadratic problems is presented. The approach reduces the primal and dual infeasibilities in each step and allows diierent stepsizes. The method is derived by investigating the eecient set of a multiobjective optimization problem. Computational results are also given.

We present asymptotically faster approximation algorithms for the generalized flow problems in which multipliers on edges are at most 1. For this lossy version of the maximum generalized flow problem, we obtain an additive ǫ approximation of the maximum flow in time Õ ( m log(U/ǫ) ) , where m is the number of edges in the graph, all capacities are integers in the range {1, . . . , U}, and all l...

We devise dynamic algorithms for the following (weak) visibility polygon computation problems: • Maintaining visibility polygon of a fixed point located interior to simple polygon amid vertex insertions and deletions to simple polygon. • Answering visibility polygon query corresponding to any point located exterior to simple polygon amid vertex insertions and deletions to simple polygon. • Main...