In this paper, we study augmented Lagrangian functions for nonlinear semidefinite programming (NSDP) problems with exactness properties. The term exact is used in the sense that the penalty parameter can be taken appropriately, so a single minimization of the augmented Lagrangian recovers a solution of the original problem. This leads to reformulations of NSDP problems … Read more
Interior-point methods have been shown to be very efficient for large-scale nonlinear programming. The combination with penalty methods increases their robustness due to the regularization of the constraints caused by the penalty term. In this paper a primal-dual penalty-interior-point algorithm is proposed, that is based on an augmented Lagrangian approach with an l2-exact penalty function. … Read more
This paper introduces a derivative-free and ready-to-use solver for nonlinear programs with nonlinear equality and inequality constraints (NLPs). Using finite differences and a sequential quadratic programming (SQP) approach, the algorithm aims at finding a local minimizer and no extra attempt is made to generate a globally optimal solution. Due to the use of finite differences, … Read more
Cutting planes are derived from specific problem structures, such as a single linear constraint from an integer program. This paper introduces cuts that involve minimal structural assumptions, enabling the generation of strong polyhedral relaxations for a broad class of problems. We consider valid inequalities for the set $S\cap P$, where $S$ is a closed set, … Read more
Bilevel problems model instances with a hierarchical structure. Aiming at an efficient solution of a constrained multiobjective problem according with some pre-defined criterion, we reformulate this optimization but non standard problem as a classic bilevel one. This reformulation intents to encompass all the objectives, so that the properly efficient solution set is recovered by means … Read more
The main task of genetic regulatory networks is to construct a sparse probabilistic Boolean network (PBN) based on a given transition-probability matrix and a set of Boolean networks (BNs). In this paper, a Bregman alternating direction method of multipliers (BADMM) is proposed to solve the minimization problem raised in PBN. All the customized subproblem-solvers of … Read more
In this paper, we consider multi-objective optimization problems involving not necessarily convex constraints and componentwise generalized-convex (e.g., semi-strictly quasi-convex, quasi-convex, or explicitly quasi-convex) vector-valued objective functions that are acting between a real linear topological pre-image space and a finite dimensional image space. For these multi-objective optimization problems, we show that the set of (strictly, weakly) … Read more
Under the strongly convex assumption, several recent works studied the global linear convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions and a non-smooth convex function. In this paper, under the quadratic growth condition{a strictly weaker condition than the strongly convex assumption, … Read more
In this paper, an augmented Lagrangian proximal alternating (ALPA) method is proposed for two class of large-scale sparse discrete constrained optimization problems in which a sequence of augmented Lagrangian subproblems are solved by utilizing proximal alternating linearized minimization framework and sparse projection techniques. Under the Mangasarian-Fromovitz and the basic constraint qualification, we show that any … Read more
We study the problem of computing weighted analytic center for system of linear matrix inequality constraints. The problem can be solved using the Standard Newton’s method. However, this approach requires that a starting point in the interior point of the feasible region be given or a Phase I problem be solved. We address the problem … Read more