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The capacitated tree cover problem with edge loads is a variant of the tree cover problem, where we are given facility opening costs, edge costs and loads, as well as vertex loads. We try to find a tree cover of minimum cost such that the…
This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, they lack optimization techniques that guarantee global optimality in…
In this paper, we address a variant of the marketing mix optimization (MMO) problem which is commonly encountered in many industries, e.g., retail and consumer packaged goods (CPG) industries. This problem requires the spend for each…
In this paper, we study the generalized problem that minimizes or maximizes a multi-order complex quadratic form with constant-modulus constraints on all elements of its optimization variable. Such a mathematical problem is commonly…
We are interested in the problem of guarding simple orthogonal polygons with the minimum number of $ r $-guards. The interior point $ p $ belongs an orthogonal polygon $ P $ is visible from $ r $-guard $ g $, if the minimum area rectangle…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…
We investigate the problem of privacy preserving distributed matrix multiplication in edge networks using multi-party computation (MPC). Coded multi-party computation (CMPC) is an emerging approach to reduce the required number of workers…
The problem of constrained reinforcement learning (CRL) holds significant importance as it provides a framework for addressing critical safety satisfaction concerns in the field of reinforcement learning (RL). However, with the introduction…
Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains…
We consider the problem of learning control policies that optimize a reward function while satisfying constraints due to considerations of safety, fairness, or other costs. We propose a new algorithm, Projection-Based Constrained Policy…
For the numerical solution of shape optimization problems, particularly those constrained by partial differential equations (PDEs), the quality of the underlying mesh is of utmost importance. Particularly when investigating complex…
We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with $n$ vertices. We give exact algorithms that solve these problems in time…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
We consider the Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families $\calR$ where $R_1 \setminus R_2$…
In today's construction industry, poor performance often arises due to various factors related to time, finances, and quality. These factors frequently lead to project delays and resource losses, particularly in terms of financial…
We propose novel randomized geometric tools to detect low-volatility anomalies in stock markets; a principal problem in financial economics. Our modeling of the (detection) problem results in sampling and estimating the (relative) volume of…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
A number of optimal decision problems with uncertainty can be formulated into a stochastic optimal control framework. The Least-Squares Monte Carlo (LSMC) algorithm is a popular numerical method to approach solutions of such stochastic…
Expensive multi-objective optimization problems can be found in many real-world applications, where their objective function evaluations involve expensive computations or physical experiments. It is desirable to obtain an approximate Pareto…
Zero-shot hyperparameter optimization (HPO) is a simple yet effective use of transfer learning for constructing a small list of hyperparameter (HP) configurations that complement each other. That is to say, for any given dataset, at least…