相关论文: Global Optimal Solution to Discrete Value Selectio…

In this paper we present the solver DuQuad specialized for solving general convex quadratic problems arising in many engineering applications. When it is difficult to project on the primal feasible set, we use the (augmented) Lagrangian…

We consider the NP-hard problem of minimizing a separable concave quadratic function over the integral points in a polyhedron, and we denote by D the largest absolute value of the subdeterminants of the constraint matrix. In this paper we…

This paper mainly addresses the Monge mass transfer problem in the 1-D case. Through an ingenious approximation mechanism, one transforms the Monge problem into a sequence of minimization problems, which can be converted into a sequence of…

This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…

A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…

Topology optimization for general materials is correctly formulated as a bi-level knapsack problem, which is considered to be NP-hard in global optimization and computer science. By using canonical duality theory (CDT) developed by the…

This paper develops a continuous-time primal-dual accelerated method with an increasing damping coefficient for a class of convex optimization problems with affine equality constraints. This paper analyzes critical values for parameters in…

Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms…

A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…

We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…

We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…

Complex system design problems, such as those involved in aerospace engineering, require the use of numerically costly simulation codes in order to predict the performance of the system to be designed. In this context, these codes are often…

In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…

We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent…

Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…

We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing…

This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with…

We analyze the question of deciding whether a quadratic or a hyperbolic 0-1 programming instance has a unique optimal solution. Both uniqueness questions are known to be NP-hard, but are unlikely to be contained in the class NP. We…

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…

In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This…