MultiRTA: A simple yet accurate method for predicting peptide binding affinities for multiple class II MHC allotypes

Categories Biomedical Applications

Background: The binding of peptide fragments of antigens to class II MHC is a crucial step in initiating a helper T cell immune response. The identification of such peptide epitopes has potential applications in vaccine design and in better understanding autoimmune diseases and allergies. However, comprehensive experimental determination of peptide-MHC binding affinities is infeasible due … Read more

Convergence rate of inexact proximal point methods with relative error criteria for convex optimization

Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

In this paper, we consider a class of inexact proximal point methods for convex optimization which allows a relative error tolerance in the approximate solution of each proximal subproblem. By exploiting the special structure of convex optimization problems, we are able to derive surprising complexity bounds for the aforementioned class. As a consequence, we show … Read more

Iteration-complexity of block-decomposition algorithms and the alternating minimization augmented Lagrangian method

Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization Tags , , , , , ,

In this paper, we consider the monotone inclusion problem consisting of the sum of a continuous monotone map and a point-to-set maximal monotone operator with a separable two-block structure and introduce a framework of block-decomposition prox-type algorithms for solving it which allows for each one of the single-block proximal subproblems to be solved in an … Read more

Pattern-Based Modeling and Solution of Probabilistically Constrained Optimization Problems

Categories Stochastic Programming

optimization problems in which the random variables are represented by an extremely large number of scenarios. The method involves the binarization of the probability distribution, and the generation of a consistent partially defined Boolean function (pdBf) representing the combination (F,p) of the binarized probability distribution F and the enforced probability level p. We show that … Read more

Robust capacity expansion solutions for telecommunication networks with uncertain demands

Categories Network Optimization, Robust Optimization, Telecommunications Tags , ,

We consider the capacity planning of telecommunication networks with linear investment costs and uncertain future traffic demands. Transmission capacities must be large enough to meet, with a high quality of service, the range of possible demands, after adequate routings of messages on the created network. We use the robust optimization methodology to balance the need … Read more

Computational and Economic Limitations of Dispatch Operations in the Next-Generation Power Grid

Categories Dynamic Programming, Linear Programming, Production and Logistics Tags , , , , ,

We study the interactions between computational and economic performance of dispatch operations under highly dynamic environments. In particular, we discuss the need for extending the forecast horizon of the dispatch formulation in order to anticipate steep variations of renewable power and highly elastic loads. We present computational strategies to solve the increasingly larger optimization problems … Read more

On Doubly Positive Semidefinite Programming Relaxations

Categories Quadratic Programming, Semi-definite Programming Tags ,

Recently, researchers have been interested in studying the semidefinite programming (SDP) relaxation model, where the matrix is both positive semidefinite and entry-wise nonnegative, for quadratically constrained quadratic programming (QCQP). Comparing to the basic SDP relaxation, this doubly-positive SDP model possesses additional O(n2) constraints, which makes the SDP solution complexity substantially higher than that for the … Read more

Two stage stochastic equilibrium problems with equilibrium constraints: modeling and numerical schemes

Categories Complementarity and Variational Inequalities, Game Theory, Stochastic Programming Tags , , ,

This paper presents a two stage stochastic equilibrium problem with equilibrium constraints(SEPEC) model. Some source problems which motivate the model are discussed. Monte Carlo sampling method is applied to solve the SEPEC. The convergence analysis on the statistical estimators of Nash equilibria and Nash stationary points are presented. ArticleDownload View PDF

Some Results on the Strength of Relaxations of Multilinear Functions

Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , ,

We study approaches for obtaining convex relaxations of global optimization problems containing multilinear functions. Specifically, we compare the concave and convex envelopes of these functions with the relaxations that are obtained with a standard relaxation approach, due to McCormick. The standard approach reformulates the problem to contain only bilinear terms and then relaxes each term … Read more

Randomized heuristics for the regenerator location problem

Categories Meta Heuristics, Network Optimization, Telecommunications Tags , , , ,

Telecommunication systems make use of optical signals to transmit information. The strength of a signal in an optical network deteriorates and loses power as it gets farther from the source, mainly due to attenuation. Therefore, to enable the signal to arrive at its intended destination with good quality, it is necessary to regenerate it periodically … Read more