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We consider two-stage robust optimization problems, which can be seen as games between a decision maker and an adversary. After the decision maker fixes part of the solution, the adversary chooses a scenario from a specified uncertainty…
Optimization via simulation has been well established to find optimal solutions and designs in complex systems. However, it still faces modeling and computational challenges when extended to the multi-stage setting. This survey reviews the…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex…
Bayesian optimization is a sample-efficient method for solving expensive, black-box optimization problems. Stochastic programming concerns optimization under uncertainty where, typically, average performance is the quantity of interest. In…
Bayesian optimization offers a flexible framework to optimize an objective function that is expensive to be evaluated. A Bayesian optimizer iteratively queries the function values on its carefully selected points. Subsequently, it makes a…
This study aims to optimize the evaluation metric of multimodal multi-objective optimization problems using a Regionalized Metric Framework, which provides a certain boost to research in this field. Existing evaluation metrics usually use…
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little…
In general, a multi-objective optimization problem does not have a single optimal solution but a set of Pareto optimal solutions, which forms the Pareto front in the objective space. Various evolutionary algorithms have been proposed to…
In this paper, we solve a maximization problem where the objective function is quadratic and convex or concave and the constraints set is the reachable value set of a convergent discrete-time affine system. Moreover, we assume that the…
For a given polyhedral convex set-valued mapping we define a polyhedral convex cone which we call the natural ordering cone. We show that the solution behavior of a polyhedral convex set optimization problem can be characterized by this…
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…
This paper explores a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraints are known. We allow the objective and constraint function to…
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
In multi-objective optimization, computing the entire non-dominated set (also known as the Pareto front or the Pareto frontier) is often intractable. However, for any multiplicative factor greater than one, an approximation set can be…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
Focusing on identification, this paper develops a class of convex optimization-based criteria and correspondingly the recursive algorithms to estimate the parameter vector $\theta^{*}$ of a stochastic dynamic system. Not only do the…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…