相关论文: A Newton-bracketing method for a simple conic opti…

In this paper, we propose a globally convergent Newton type method to solve $\ell_0$ regularized sparse optimization problem. In fact, a line search strategy is applied to the Newton method to obtain global convergence. The Jacobian matrix…

We consider the exact solution of problem $(QP)$ that consists in minimizing a quadratic function subject to quadratic constraints. Starting from the classical convex relaxation that uses the McCormick's envelopes, we introduce 12…

In this paper, we present several new linearizations of a quadratic binary optimization problem (QBOP), primarily using the method of aggregations. Although aggregations were studied in the past in the context of solving system of…

In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…

Computing the regularized solution of Bayesian linear inverse problems as well as the corresponding regularization parameter is highly desirable in many applications. This paper proposes a novel iterative method, termed the Projected Newton…

The continuous quadratic knapsack (CQK) problem involves minimizing a diagonal convex quadratic function subject to box constraints and a single linear equality constraint. It has numerous applications in resource allocation, multicommodity…

We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…

The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…

In this paper the simplicial cone constrained convex quadratic programming problem is studied. The optimality conditions of this problem consist in a linear complementarity problem. This fact, under a suitable condition, leads to an…

We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…

We consider the chance-constrained binary knapsack problem (CKP), where the item weights are independent and normally distributed. We introduce a continuous relaxation for the CKP, represented as a non-convex optimization problem, which we…

The problem of interest is the minimization of a nonlinear function subject to nonlinear equality constraints using a sequential quadratic programming (SQP) method. The minimization must be performed while observing only noisy evaluations…

Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible…

The Standard Quadratic optimization Problem (StQP), arguably the simplest among all classes of NP-hard optimization problems, consists of extremizing a quadratic form (the simplest nonlinear polynomial) over the standard simplex (the…

In this paper, we present an efficient semismooth Newton method, named SSNCP, for solving a class of semidefinite programming problems. Our approach is rooted in an equivalent semismooth system derived from the saddle point problem induced…

We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…

Optimization problems, arise in many practical applications, from the view points of both theory and numerical methods. Especially, significant improvement in deep learning training came from the Quasi-Newton methods. Quasi-Newton search…

We propose a solution approach for the problem (P) of minimizing an unconstrained binary polynomial optimization problem. We call this method PQCR (Polynomial Quadratic Convex Reformulation). The resolution is based on a 3-phase method. The…

This paper addresses the challenge of developing efficient algorithms for large-scale nonconvex multiobjective optimization problems (MOPs). While quasi-Newton methods are effective, their traditional application to MOPs is computationally…