Related papers: Sequential Relaxation of Unit Commitment with AC T…

For general quadratically-constrained quadratic programming (QCQP), we propose a parabolic relaxation described with convex quadratic constraints. An interesting property of the parabolic relaxation is that the original non-convex feasible…

Power systems Unit Commitment (UC) problem determines the generator commitment schedule and dispatch decisions for power networks based on forecasted electricity demand. However, with the increasing penetration of renewables and stochastic…

Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in…

Signomial geometric programming (SGP) is a computationally challenging, NP-Hard class of nonconvex nonlinear optimization problems. SGP can be solved iteratively using a sequence of convex relaxations; consequently, the strength of such…

The rapid growth of data centers increasingly requires data center operators to "bring own generation" to complement the available utility power plants to supply all or part of data center load. This practice sharply increases the number of…

The scenario approach is a general data-driven algorithm to chance-constrained optimization. It seeks the optimal solution that is feasible to a carefully chosen number of scenarios. A crucial step in the scenario approach is to compute the…

In this paper we consider the problem of maximizing the Area under the ROC curve (AUC) which is a widely used performance metric in imbalanced classification and anomaly detection. Due to the pairwise nonlinearity of the objective function,…

Nonlinear dynamics and safety constraints typically result in a nonlinear programming problem when applying model predictive control to achieve safe output consensus. To avoid the heavy computational burden of solving a nonlinear…

Direct-current microgrids (DC-MGs) can operate in either grid-connected or stand-alone mode. In particular, stand-alone DC-MG has many distinct applications. However, the optimal power flow problem of a stand-alone DC-MG is inherently…

We propose a novel decomposition framework for the distributed optimization of Difference Convex (DC)-type nonseparable sum-utility functions subject to coupling convex constraints. A major contribution of the paper is to develop for the…

The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…

This paper considers the decentralized convex optimization problem, which has a wide range of applications in large-scale machine learning, sensor networks, and control theory. We propose novel algorithms that achieve optimal computation…

Convex relaxations of the power flow equations and, in particular, the Semi-Definite Programming (SDP), Second-Order Cone (SOC), and Convex DistFlow (CDF) relaxations, have attracted significant interest in recent years. Thus far, studies…

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

In this paper we address the speed planning problem for a vehicle over an assigned path with the aim of minimizing a weighted sum of travel time and energy consumption under suitable constraints (maximum allowed speed, maximum traction or…

This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…

Integrated sensing and communication (ISAC) is expected to be offered as a fundamental service in the upcoming sixth-generation (6G) communications standard. However, due to the exposure of information-bearing signals to the sensing…

Alternating current optimal power flow (AC OPF) is one of the most fundamental optimization problems in electrical power systems. It can be formulated as a semidefinite program (SDP) with rank constraints. Solving AC OPF, that is, obtaining…

We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…

This work addresses the ecological-adaptive cruise control problem for connected electric vehicles by a computationally efficient robust control strategy. The problem is formulated in the space-domain with a realistic description of the…