A Levenberg-Marquardt method with approximate projections
The projected Levenberg-Marquardt method for the solution of a system of equations with convex constraints is known to converge locally quadratically to a possibly nonisolated solution if a certain error bound condition holds. This condition turns out ...
Faster, but weaker, relaxations for quadratically constrained quadratic programs
We introduce a new relaxation framework for nonconvex quadratically constrained quadratic programs (QCQPs). In contrast to existing relaxations based on semidefinite programming (SDP), our relaxations incorporate features of both SDP and second order ...
Convergence of the reweighted ℓ1 minimization algorithm for ℓ2---ℓp minimization
The iteratively reweighted ℓ 1 minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is ...
A new error bound result for Generalized Nash Equilibrium Problems and its algorithmic application
We present a new algorithm for the solution of Generalized Nash Equilibrium Problems. This hybrid method combines the robustness of a potential reduction algorithm and the local quadratic convergence rate of the LP-Newton method. We base our local ...
Non-cooperative games with minmax objectives
We consider noncooperative games where each player minimizes the sum of a smooth function, which depends on the player, and of a possibly nonsmooth function that is the same for all players. For this class of games we consider two approaches: one based ...
On an enumerative algorithm for solving eigenvalue complementarity problems
In this paper, we discuss the solution of linear and quadratic eigenvalue complementarity problems (EiCPs) using an enumerative algorithm of the type introduced by Júdice et al. (Optim. Methods Softw. 24:549---586, 2009 ). Procedures for computing the ...
Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach
This paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We ...
An affine scaling method for optimization problems with polyhedral constraints
Recently an affine scaling, interior point algorithm ASL was developed for box constrained optimization problems with a single linear constraint (Gonzalez-Lima et al., SIAM J. Optim. 21:361---390, 2011 ). This note extends the algorithm to handle more ...
Exact computational approaches to a stochastic uncapacitated single allocation p-hub center problem
The stochastic uncapacitated single allocation p-hub center problem is an extension of the deterministic version which aims to minimize the longest origin-destination path in a hub and spoke network. Considering the stochastic nature of travel times on ...
On error bounds and Newton-type methods for generalized Nash equilibrium problems
Error bounds (estimates for the distance to the solution set of a given problem) are key to analyzing convergence rates of computational methods for solving the problem in question, or sometimes even to justifying convergence itself. That said, for the ...
Approximation methods for complex polynomial optimization
Complex polynomial optimization problems arise from real-life applications including radar code design, MIMO beamforming, and quantum mechanics. In this paper, we study complex polynomial optimization models where the objective function takes one of the ...
Convergence properties of the inexact Lin-Fukushima relaxation method for mathematical programs with complementarity constraints
Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, form a difficult class of optimization problems. The feasible set of MPECs is described by standard equality and inequality constraints as well as additional ...
A constrained optimization reformulation and a feasible descent direction method for $$L_{1/2}$$L1/2 regularization
In this paper, we first propose a constrained optimization reformulation to the $$L_{1/2}$$ L 1 / 2 regularization problem. The constrained problem is to minimize a smooth function subject to some quadratic constraints and nonnegative constraints. A good property of the ...
Optimal parameter selection for nonlinear multistage systems with time-delays
In this paper, we consider a novel dynamic optimization problem for nonlinear multistage systems with time-delays. Such systems evolve over multiple stages, with the dynamics in each stage depending on both the current state of the system and the state ...
Space tensor conic programming
Space tensors appear in physics and mechanics. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research area of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive ...
A regularized Newton method without line search for unconstrained optimization
In this paper, we propose a regularized Newton method without line search. The proposed method controls a regularization parameter instead of a step size in order to guarantee the global convergence. We show that the proposed algorithm has the following ...
A smoothing augmented Lagrangian method for solving simple bilevel programs
In this paper, we design a numerical algorithm for solving a simple bilevel program where the lower level program is a nonconvex minimization problem with a convex set constraint. We propose to solve a combined problem where the first order condition ...
Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach
In this paper we consider cardinality-constrained convex programs that minimize a convex function subject to a cardinality constraint and other linear constraints. This class of problems has found many applications, including portfolio selection, subset ...