Related papers: Refined Shapley-Folkman Lemma and Its Application …
In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…
We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…
In this paper we present a unifying framework for continuous optimization methods grounded in the concept of generalized convexity. Utilizing the powerful theory of $\Phi$-convexity, we propose a conceptual algorithm that extends the…
This article develops duality principles applicable to the non-linear Kirchhoff-Love model of plates. The results are obtained through standard tools of convex analysis, functional analysis, calculus of variations and duality theory. The…
We revisit the standard ``telescoping sum'' argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of…
Recently, Yamanaka and Yamashita proposed the so-called positively homogeneous optimization problem, which includes many important problems, such as the absolute-value and the gauge optimizations. They presented a closed form of the dual…
This paper develops a highly general convex duality framework for the perturbed utility route choice (PURC) model. We show that the traveler's constrained, potentially non-smooth utility maximization problem admits a dual formulation: an…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust…
A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes…
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
We consider nonsmooth optimization problems under affine constraints, where the objective consists of the average of the component functions of a large number $N$ of agents, and we only assume access to the Fenchel conjugate of the…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization…
We propose an enhanced zeroth-order stochastic Frank-Wolfe framework to address constrained finite-sum optimization problems, a structure prevalent in large-scale machine-learning applications. Our method introduces a novel double variance…
We propose a flexible yet interpretable model for high-dimensional data with time-varying second order statistics, motivated and applied to functional neuroimaging data. Motivated by the neuroscience literature, we factorize the covariances…
We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality…
In this work, we consider a constrained convex problem with linear inequalities and provide an inexact penalty re-formulation of the problem. The novelty is in the choice of the penalty functions, which are smooth and can induce a non-zero…