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This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…

Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…

This paper considers the stochastic convex composite optimization problem and presents multi-cut stochastic approximation (SA) methods for solving it, whose models in expectation overestimate its objective function. The multi-cut model…

Trimming is a core technique in geometric modeling. Unfortunately, the resulting objects do not take the requirements of numerical simulations into account and yield various problems. This paper outlines principal issues of trimmed models…

Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

Cutting planes are crucial in solving mixed integer linear programs (MILP) as they facilitate bound improvements on the optimal solution. Modern MILP solvers rely on a variety of separators to generate a diverse set of cutting planes by…

We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available…

Given a family of feasible subsets of a ground set, the packing problem is to find a largest subfamily of pairwise disjoint family members. Non-approximability renders heuristics attractive viable options, while efficient methods with…

Semi-infinite programs are a class of mathematical optimization problems with a finite number of decision variables and infinite constraints. As shown by Blankenship and Falk (Blankenship and Falk. "Infinitely constrained optimization…

We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…

We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…

We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…

We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…

In networks, there are often more than one source of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity and…

Branch and bound methods which are based on the principle "divide and conquer" are a well established solution approach in single-objective integer programming. In multi-objective optimization branch and bound algorithms are increasingly…

The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…

Error enhancement properties of data processing algorithms in elementary particle physics measurements are discussed. It is argued that a systematic use of continuous weights instead of hard cuts may reduce errors of the results at the cost…