相关论文: Duality for Composite Optimization Problem within …

We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our…

To every nearly convex optimization problem, that is a minimization problem with a nearly convex objective function and a nearly convex constraint set, we associate a uniquely defined convex optimization problem with a lower semicontinuous…

In this paper, we study a constrained utility maximization problem following the convex duality approach. After formulating the primal and dual problems, we construct the necessary and sufficient conditions for both the primal and dual…

We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…

Indicator functions of taking values of zero or one are essential to numerous applications in machine learning and statistics. The corresponding primal optimization model has been researched in several recent works. However, its dual…

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…

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…

A mixed type dual to a nondifferentiable variational problem involving higher order derivative is formulated and duality results are proved under generalized invexity conditions. Special cases are generated from our results.

This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of…

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…

The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…

We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…

In this work we present two particular cases of the general duality result for linear optimisation problems over signed measures with infinitely many constraints in the form of integrals of functions with respect to the decision variables…

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new…

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. The method is then…

We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set.…

In this thesis, we present results related to complementarity problems. We study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed…

This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly…

In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…

In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…