Solving ill-posed bilevel programs

This paper deals with ill-posed bilevel programs, i.e., problems admitting multiple lower-level solutions for some upper-level parameters. Many publications have been devoted to the standard optimistic case of this problem, where the difficulty is essentially moved from the objective function to the feasible set. This new problem is simpler but there is no guaranty to … Read more

A Preconditioner for a Primal-Dual Newton Conjugate Gradients Method for Compressed Sensing Problems

In this paper we are concerned with the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. We extend a primal-dual Newton Conjugate Gradients (pdNCG) method for CS problems. We provide an inexpensive and provably effective preconditioning technique for linear systems using pdNCG. Numerical results … Read more

Maximizing a class of submodular utility functions with constraints

Motivated by stochastic 0-1 integer programming problems with an expected utility objective, we study the mixed-integer nonlinear set: $P = \cset{(w,x)\in \reals \times \set{0,1}^N}{w \leq f(a’x + d), b’x \leq B}$ where $N$ is a positive integer, $f:\reals \mapsto \reals$ is a concave function, $a, b \in \reals^N$ are nonnegative vectors, $d$ is a real … Read more

Achieving Cost-Effective Power Grid Hardening through Transmission Network Topology Control

Vulnerability of power grid is a critical issue in power industry. In order to understand and reduce power grid vulnerability under threats, existing research often employs defender-attacker-defender (DAD) models to derive effective protection plans and evaluate grid performances under various contingencies. Transmission line switching (also known as topology control) is an effective operation to mitigate … Read more

A polynomial algorithm for linear optimization which is strongly polynomial under certain conditions on optimal solutions

This paper proposes a polynomial algorithm for linear programming which is strongly polynomial for linear optimization problems $\min\{c^Tx : Ax = b, x\ge {\bf 0}\}$ having optimal solutions where each non-zero component $x_j$ belongs to an interval of the form $[\alpha_j, \alpha_j\cdot 2^{p(n)}],$ where $\alpha_j$ is some positive value and $p(n)$ is a polynomial of … Read more

Variational principles with generalized distances and applications to behavioral sciences

This paper has a two-fold focus on proving that the quasimetric and the weak $\tau$-distance versions of the Ekeland variational principle are equivalent in the sense that one implies the other and on presenting the need of such extensions for possible applications in the formation and break of workers hiring and firing routines. Article Download … Read more

Global convergence of the Heavy-ball method for convex optimization

This paper establishes global convergence and provides global bounds of the convergence rate of the Heavy-ball method for convex optimization problems. When the objective function has Lipschitz-continuous gradient, we show that the Cesa ́ro average of the iterates converges to the optimum at a rate of $O(1/k)$ where k is the number of iterations. When … Read more

On the Adaptivity Gap in Two-stage Robust Linear Optimization under Uncertain Constraints

In this paper, we study the performance of static solutions in two-stage adjustable robust packing linear optimization problem with uncertain constraint coefficients. Such problems arise in many important applications such as revenue management and resource allocation problems where demand requests have uncertain resource requirements. The goal is to find a two-stage solution that maximizes the … Read more

Generalized Dual Face Algorithm for Linear Programming

As a natural extension of the dual simplex algorithm, the dual face algorithm performed remarkably in computational experiments with a set of Netlib standard problems. In this paper, we generalize it to bounded-variable LP problems via local duality. Citation Department of Mathematics, Southeast University, Nanjing, 210096, China, 12/2014 Article Download View Generalized Dual Face Algorithm … Read more

An asymptotic inclusion speed for the Douglas-Rachford splitting method in Hilbert spaces

In this paper, we consider the Douglas-Rachford splitting method for monotone inclusion in Hilbert spaces. It can be implemented as follows: from the current iterate, first use forward-backward step to get the intermediate point, then to get the new iterate. Generally speaking, the sum operator involved in the Douglas-Rachford splitting takes the value of every … Read more