In this paper we want to investigate the following problem: For a given upper bound for the ruin probability, maximize the expected discounted consumption of an investor in finite time. The endowment of the agent is modeled by Brownian motion with positive drift. We give an iterative algorithm for the solution of the problem, where in each step an unconstraint, but penalized, problem is solved....

One of the most efficient interior-point methods for some classes of primal block-angular problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. Its efficiency depends on the spectral radius—in [0,1)— of a certain matrix in the definition of the preconditioner. Spectral radius c...

We present a survey of nondiierentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of ...

Here we present a primal-dual interior point multidimensional filter line search method for nonlinear programming. The filter relies on a multidimensional feasibility measure enforcing every constraint violation to zero. To prevent convergence to feasible nonoptimal points a sufficient reduction criterion is also imposed on the barrier function. The evaluation of the method is until now made on...

Atmospheric turbulence is an important factor that limits the amount of attenuation a barrier can provide in the outdoor environment. It is therefore important to develop a reliable method to predict its effect on barrier performance. The boundary element method (BEM) has been shown to be a very effective technique for predicting barrier insertion loss in the absence of turbulence. This paper d...

We present a framework for designing and analyzing primal-dual interior-point methods for convex optimization. We assume that a self-concordant barrier for the convex domain of interest and the Legendre transformation of the barrier are both available to us. We directly apply the theory and techniques of interior-point methods to the given good formulation of the problem (as is, without a conic...

W consider the problem of maximizing an expected utility function of n assets, such as the mean-variance or power-utility function. Associated with a change in an asset’s holdings from its current or target value is a transaction cost. This cost must be accounted for in practical problems. A straightforward way of doing so results in a 3n-dimensional optimization problem with 3n additional cons...

An infeasible interior-point algorithm for solving the$P_*$-matrix linear complementarity problem based on a kernelfunction with trigonometric barrier term is analyzed. Each (main)iteration of the algorithm consists of a feasibility step andseveral centrality steps, whose feasibility step is induced by atrigonometric kernel function. The complexity result coincides withthe best result for infea...