By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. This new method is then extended to solve a general multi-block separable convex optimization problem, and two related primal-dual hybrid gradient algorithms are also discussed. … Read more
This paper studies optimal criteria for the appointment scheduling of outpatients in a medical imaging center. The main goal of this study is to coordinate the assignments of radiopharmaceuticals and the scheduling of outpatients on imaging scanners. We study a special case of a molecular imaging center that offers services for various diagnostic procedures for … Read more
More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum eigenvalue of a univariate real analytic Hermitian matrix family is twice continuously differentiable, with Lipschitz second derivative, at all local maximizers, a property that … Read more
This work is devoted to studying an Accelerated Stochastic Peaceman-Rachford Splitting Method (AS-PRSM) for solving a family of structural empirical risk minimization problems. The objective function to be optimized is the sum of a possibly nonsmooth convex function and a finite-sum of smooth convex component functions. The smooth subproblem in AS-PRSM is solved by a stochastic gradient method using variance reduction … Read more
We study the exact convergence rate of the alternating projection method for the nontransversal intersection of a semialgebraic set and a linear subspace. If the linear subspace is a line, the exact rates are expressed by multiplicities of the defining polynomials of the semialgebraic set, or related power series. Our methods are also applied to … Read more
In machine learning (ML) applications, unfair predictions may discriminate against a minority group. Most existing approaches for fair machine learning (FML) treat fairness as a constraint or a penalization term in the optimization of a ML model, which does not lead to the discovery of the complete landscape of the trade-offs among learning accuracy and … Read more
In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of several first-order methods designed for nonsmooth nonconvex optimization problems. Such properties guarantee the convergence of the full sequence of … Read more
We propose a new class of rigorous methods for derivative-free optimization with the aim of delivering efficient and robust numerical performance for functions of all types, from smooth to non-smooth, and under different noise regimes. To this end, we have developed Full-Low Evaluation methods, organized around two main types of iterations. The first iteration type … Read more
In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution … Read more
We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where both differentiability and nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of strongly semismooth functions. We show that the so-called local error bound condition does not hold for this system. Thus the … Read more