相关论文: Global Optimal Solution to Discrete Value Selectio…
Optimization problems with discrete decisions are nonconvex and thus lack strong duality, which limits the usefulness of tools such as shadow prices and the KKT conditions. It was shown in Burer(2009) that mixed-binary quadratic programs…
We study geometric duality for convex vector optimization problems. For a primal problem with a $q$-dimensional objective space, we formulate a dual problem with a $(q+1)$-dimensional objective space. Consequently, different from an…
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-smooth non-convex problem. In this paper, we investigate the dual forms of…
This paper considers a general convex constrained problem setting where functions are not assumed to be differentiable nor Lipschitz continuous. Our motivation is in finding a simple first-order method for solving a wide range of convex…
We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to…
We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…
We consider strongly convex optimization problems with affine-type restrictions. We build dual problem and solve dual problem by Fast Gradient Method. We use primal-dual structure of this method to construct the solution of the primal…
We propose an exact method which combines the resolution search and branch & bound algorithms for solving the 0?1 Multidimensional Knapsack Problem. This algorithm is able to prove large?scale strong correlated instances. The optimal values…
We study problems arising in real-time auction markets, common in e-commerce and computational advertising, where bidders face the problem of calculating optimal bids. We focus upon a contract management problem where a demand aggregator is…
This paper addresses a quadratic problem with assignment constraints, an NP-hard combinatorial optimization problem arisen from facility location, multiple-input multiple-output detection, and maximum mean discrepancy calculation et al. The…
An algorithm is proposed for solving optimization problems with stochastic objective and deterministic equality and inequality constraints. This algorithm is objective-function-free in the sense that it only uses the objective's gradient…
Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…
We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables.…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
In this paper, we propose a unified primal-dual algorithm framework based on the augmented Lagrangian function for composite convex problems with conic inequality constraints. The new framework is highly versatile. First, it not only covers…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
This paper aims to solve a class of CEC benchmark constrained optimization problems that have been widely studied by nature-inspired optimization algorithms. Global optimality condition based on canonical duality theory is derived.…
This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…