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We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…
In spite of the growing consideration for optimal execution in the financial mathematics literature, numerical approximations of optimal trading curves are almost never discussed. In this article, we present a numerical method to…
In this work we establish the equivalence of algorithmic regularization and explicit convex penalization for generic convex losses. We introduce a geometric condition for the optimization path of a convex function, and show that if such a…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using…
We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization,…
We propose a decentralized penalty method for general convex constrained multi-agent optimization problems. Each auxiliary penalized problem is solved approximately with a special parallel descent splitting method. The method can be…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
We consider the convex minimization model with both linear equality and inequality constraints, and reshape the classic augmented Lagrangian method (ALM) by balancing its subproblems. As a result, one of its subproblems decouples the…
The augmented Lagrangian method (ALM) is a classical optimization tool that solves a given "difficult" (constrained) problem via finding solutions of a sequence of "easier"(often unconstrained) sub-problems with respect to the original…
Our work focuses on stochastic gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer. Research on this class of problem is quite limited, and until recently no non-asymptotic convergence…
Multi-agent distributed optimization over a network minimizes a global objective formed by a sum of local convex functions using only local computation and communication. We develop and analyze a quantized distributed algorithm based on the…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
This short note provides a systematic construction of market models without unbounded profits but with arbitrage opportunities.
This paper presents GeNI-ADMM, a framework for large-scale composite convex optimization that facilitates theoretical analysis of both existing and new approximate ADMM schemes. GeNI-ADMM encompasses any ADMM algorithm that solves a first-…
This paper introduces a novel approach to solving multi-block nonconvex composite optimization problems through a proximal linearized Alternating Direction Method of Multipliers (ADMM). This method incorporates an Increasing Penalization…
This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…