Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in vectorial form. In this survey we discuss the fundamental problem of mapping graphs to vectors, and its … Read more
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal solution, a special nearly low-rank form of all primal iterates is imposed. To accommodate such a (restrictive) … Read more
A concentrated solar tower power plant consists of a receiver mounted atop of a central tower and a field of movable mirrors called heliostats. The heliostats concentrate solar radiation onto the receiver where a fluid is heated to produce electricity in a conventional thermodynamic cycle. Aiming strategies are used to assign each heliostat to an … Read more
Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource’s capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing … Read more
In some applications the considered multistage stochastic programs have a periodical behavior. We show that in such cases it is possible to drastically reduce the number of stages by introducing a periodical analog of the so-called Bellman equations for discounted infinite horizon problems, used in Markov Decision Processes and Stochastic Optimal Control. Furthermore, we describe … Read more
Tailored mixed-integer optimal control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems by solving one continuous nonlinear program and one mixed-integer linear program. … Read more
For sparse graphs, the odd cycle polytope can be used to compute useful bounds for the maximum stable set problem quickly. Yannakakis introduced an extended formulation for the odd cycle inequalities of the stable set polytope in 1991, which provides a direct way to optimize over the odd cycle polytope in polynomial time, although there … Read more
Stochastic gradient method and its variants are simple yet effective for minimizing an expectation function over a closed convex set. However, none of these methods are applicable to solve stochastic programs with expectation constraints, since the projection onto the feasible set is prohibitive. To deal with the expectation constrained stochastic convex optimization problems, we propose … Read more
A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables in a different subset are constrained to remain in a convex set. The proposed algorithm exploits the structure by combining steps … Read more
We consider a problem involving a set of agents who need to coordinate their actions to optimize the sum of their objectives while satisfying a common resource constraint. The objective functions of the agents are unknown to them a priori and are revealed in an online manner. The resulting problem is an online optimization problem … Read more