A deep cut ellipsoid algorithm for convex programming

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported

Oracle-based optimization applied to climate model calibration

In this paper, we show how oracle-based optimization can be effectively used for the calibration of an intermediate complexity climate model. In a fully developed example, we estimate the 12 principal parameters of the C-GOLDSTEIN climate model by using an oracle- based optimization tool, Proximal-ACCPM. The oracle is a procedure that finds, for each query point, a value for the goodness-of-fit function and an evaluation of its gradient. The difficulty in the model calibration problem stems from the need to undertake costly calculations for each simulation and also from the fact that the error function used to assess the goodness-of-fit is not convex. The method converges to a Fbest fit_ estimate over 10 times faster than a comparable test using the ensemble Kalman filter. The approach is simple to implement and potentially useful in calibrating computationally demanding models based on temporal integration (simulation), for which functional derivative information is not readily available

An In-Out Approach to Disjunctive Optimization

Abstract. Cutting plane methods are widely used for solving convex optimization problems and are of fundamental importance, e.g., to pro-vide tight bounds for Mixed-Integer Programs (MIPs). This is obtained by embedding a cut-separation module within a search scheme. The importance of a sound search scheme is well known in the Constraint Programming (CP) community. Unfortunately, the “standard ” search scheme typically used for MIP problems, known as the Kelley method, is often quite unsatisfactory because of saturation issues. In this paper we address the so-called Lift-and-Project closure for 0-1 MIPs associated with all disjunctive cuts generated from a given set of elementary disjunction. We focus on the search scheme embedding the generated cuts. In particular, we analyze a general meta-scheme for cutting plane algorithms, called in-out search, that was recently proposed by Ben-Ameur and Neto [1]. Computational results on test instances from the literature are presented, showing that using a more clever meta-scheme on top of a black-box cut generator may lead to a significant improvement

Home dialysis: conclusions from a Kidney Disease: Improving Global Outcomes (KDIGO) controversies conference

Home dialysis modalities (home hemodialysis [HD] and peritoneal dialysis [PD]) are associated with greater patient autonomy and treatment satisfaction compared with in-center modalities, yet the level of home-dialysis use worldwide is low. Reasons for limited utilization are context-dependent, informed by local resources, dialysis costs, access to healthcare, health system policies, provider bias or preferences, cultural beliefs, individual lifestyle concerns, potential care-partner time, and financial burdens. In May 2021, KDIGO (Kidney Disease: Improving Global Outcomes) convened a controversies conference on home dialysis, focusing on how modality choice and distribution are determined and strategies to expand home-dialysis use. Participants recognized that expanding use of home dialysis within a given health system requires alignment of policy, fiscal resources, organizational structure, provider incentives, and accountability. Clinical outcomes across all dialysis modalities are largely similar, but for specific clinical measures, one modality may have advantages over another. Therefore, choice among available modalities is preference-sensitive, with consideration of quality of life, life goals, clinical characteristics, family or care-partner support, and living environment. Ideally, individuals, their care-partners, and their healthcare teams will employ shared decision-making in assessing initial and subsequent kidney failure treatment options. To meet this goal, iterative, high-quality education and support for healthcare professionals, patients, and care-partners are priorities. Everyone who faces dialysis should have access to home therapy. Facilitating universal access to home dialysis and expanding utilization requires alignment of policy considerations and resources at the dialysis-center level, with clear leadership from informed and motivated clinical teams

A Two-Cut Aproach in the Analytic Center Cutting Plane Method.

We analyze the process of a two cut generation scheme in the analytic center cutting plane method. We propose an optimal restoration when the two cuts are central.MATHEMATICS

A Nonlinear Analytic Center Cutting Plane Method For A Class Of Convex Programming Problems

. A cutting plane algorithm for minimizing a convex function subject to constraints defined by a separation oracle is presented. The algorithm is based on approximate analytic centers. The nonlinearity of the objective function is taken into account, yet the feasible region is approximated by a containing polytope. This containing polytope is regularly updated by adding a new cut through a test point. Each test point is an approximate analytic center of the intersection of a containing polytope and a level set of the nonlinear objective function. We establish the complexity of the algorithm. Our complexity estimate is given in terms of the problem dimension, the desired accuracy of an approximate solution and other parameters that depend on the geometry of a specific instance of the problem. Key words. convex programming, interior-point methods, analytic center, cutting planes, potential function, self-concordance AMS subject classifications. 90C06, 90C25 1. Introduction. Recently, ..