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This research concerns design optimization problems involving numerous design parameters and large computational models. These problems generally consist in non-convex constrained optimization problems in large and sometimes complex search…
This paper focuses on the problem of energy imbalance management in amicrogrid. The problem is investigated from the power market perspective. Unlike the traditional power grid, a microgrid can obtain extra energy froma renewable energy…
A class of smoothing methods is proposed for solving mathematical programs with equimibrium constraints. We introduce new and very simple regularizations of the complementarity constraints. Some estimate distance to optimal solution and…
We consider scalar equilibrium problems governed by a bifunction in a finite-dimensional framework. By using classical arguments in Convex Analysis, we show that under suitable generalized convexity assumptions imposed on the bifunction,…
The massive integration of distributed energy resources changes the operational demands of the electric power distribution system, motivating optimization-based approaches. The added computational complexities of the resulting optimal power…
We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…
This paper investigates the feasibility of using a discriminate pricing scheme to offset the inconvenience that is experienced by an energy user (EU) in trading its energy with an energy controller in smart grid. The main objective is to…
We propose new results for the existence and uniqueness of a general nonparametric and nonseparable competitive equilibrium with substitutes. These results ensure the invertibility of a general competitive system. The existing literature…
The demand response provides an opportunity for load serving entities (LSEs) that operate retail electricity markets (REMs) to strategically purchase energy and provide reserves in wholesale electricity markets (WEMs). This paper concerns…
We show an auction-based algorithm to compute market equilibrium prices in a production model, where consumers purchase items under separable nonlinear utility concave functions which satisfy W.G.S(Weak Gross Substitutes); producers produce…
The presence of uncertainties in the ride-hailing market complicates the pricing strategies of on-demand platforms that compete each other to offer a mobility service while striving to maximize their profit. Looking at this problem as a…
We propose an algorithm to calculate the exact solution for utility optimization problems on finite state spaces under a class of non-differentiable preferences. We prove that optimal strategies must lie on a discrete grid in the plane, and…
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known…
Curve fitting is a fundamental technique in engineering and scientific research, serving as a critical tool for extracting insights from data. This study explores the application of various statistical equations to estimate outcomes in…
Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…
This paper studies the topic of cost-efficiency in incomplete markets. A payoff is called cost-efficient if it achieves a given probability distribution at some given investment horizon with a minimum initial budget. Extensive literature…
The Fisher market is one of the most fundamental models for resource allocation problems in economic theory, wherein agents spend a budget of currency to buy goods that maximize their utilities, while producers sell capacity constrained…
In the restructured electricity industry, electricity pooling markets are an oligopoly with strategic producers possessing private information (private production cost function). We focus on pooling markets where aggregate demand is…
This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the…
Our paper aims to model supply and demand curves of electricity day-ahead auction in a parsimonious way. Our main task is to build an appropriate algorithm to present the information about electricity prices and demands with far less…