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Building on ideas from online convex optimization, we propose a general framework for the design of efficient securities markets over very large outcome spaces. The challenge here is computational. In a complete market, in which one…
We introduce a new class of semidefinite programming (SDP) relaxations for sparse box-constrained quadratic programs, obtained by a novel integration of the Reformulation Linearization Technique into standard SDP relaxations while…
This paper deals with the non-convex power system state estimation (PSSE) problem, which plays a central role in the monitoring and operation of electric power networks. Given a set of noisy measurements, PSSE aims at estimating the vector…
Many nonconvex problems in robotics can be relaxed into convex formulations via Semi-Definite Programming (SDP) that can be solved to global optimality. The practical quality of these solutions, however, critically depends on rounding them…
Hydro-thermal coordination is the problem of determining the optimal economic dispatch of hydro and thermal power plants over time. The physics of hydroelectricity generation is commonly simplified in the literature to account for its…
This paper proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem,…
Although the specific structures of electricity markets are diverse around the world, they were all conceived on the premise of predictable, controllable generation with nonnegligible marginal costs. Recent changes, specifically, the…
Determination of the most economic strategies for supply and transmission of electricity is a daunting computational challenge. Due to theoretical barriers, so-called NP-hardness, the amount of effort to optimize the schedule of generating…
This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…
We study the maximization of sums of heterogeneous quadratic forms over the Stiefel manifold, a nonconvex problem that arises in several modern signal processing and machine learning applications such as heteroscedastic probabilistic…
Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
A power market with non-convexities may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, the market players are entitled to receive the uplift payments that…
The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold…
Convex relaxation methods are powerful tools for studying the lowest energy of many-body problems. By relaxing the representability conditions for marginals to a set of local constraints, along with a global semidefinite constraint, a…
Economic dispatch problem for a networked power system has been considered. The objective is to minimize the total generation cost while meeting the overall supply-demand balance and generation capacity. In particular, a more practical…
Electricity storage is used for intertemporal price arbitrage and for ancillary services that balance unforeseen supply and demand fluctuations via frequency regulation. We present an optimization model that computes bids for both arbitrage…
In this paper, we propose two algorithms for nonlinear semi-infinite semi-definite programs with infinitely many convex inequality constraints, called SISDP for short. A straightforward approach to the SISDP is to use classical methods for…
In electricity markets, customers are increasingly constrained by their budgets. A budget constraint for a user is an upper bound on the price multiplied by the quantity. However, since prices are determined by the market equilibrium, the…
Although neural networks have been applied to several systems in recent years, they still cannot be used in safety-critical systems due to the lack of efficient techniques to certify their robustness. A number of techniques based on convex…
This paper demonstrates a practical method for computing the solution of an expectation-constrained robust maximization problem with immediate applications to model-free no-arbitrage bounds and super-replication values for many financial…