Related Work on Geometry of Non-Convex Programs

2019 ◽  
pp. 39-44
Author(s):  
Bin Shi ◽  
S. S. Iyengar
Keyword(s):  
Convex Programs

Further Development in the Global Resolution of Convex Programs with Complementarity Constraints

2014 ◽  
Author(s):  
John E. Mitchell ◽  
Jong-Shi Pang ◽  
Yu-Ching Lee ◽  
Bin Yu ◽  
Lijie Bai
Keyword(s):  
Complementarity Constraints ◽  
Convex Programs ◽  
Further Development

scholarly journals Successive convex approximations to cardinality-constrained convex programs: a piecewise-linear DC approach

2013 ◽  
Vol 59 (1-2) ◽  
pp. 379-397 ◽  
Author(s):  
Xiaojin Zheng ◽  
Xiaoling Sun ◽  
Duan Li ◽  
Jie Sun
Keyword(s):  
Piecewise Linear ◽  
Convex Programs ◽  
Convex Approximations

scholarly journals Exact solutions of infinite dimensional total-variation regularized problems

2018 ◽  
Vol 8 (3) ◽  
pp. 407-443 ◽  
Author(s):  
Axel Flinth ◽  
Pierre Weiss
Keyword(s):  
Inverse Problems ◽  
Exact Solutions ◽  
Total Variation ◽  
Linear Mapping ◽  
Scattered Data Approximation ◽  
Convex Programs ◽  
Linear Measurements ◽  
Data Approximation ◽  
Infinite Dimensional ◽  
Finite Dimensional

Abstract We study the solutions of infinite dimensional inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary function. The first contribution describes the solution’s structure: we show that under mild assumptions, there always exists an $m$-sparse solution, where $m$ is the number of linear measurements of the signal. Our second contribution is about the computation of the solution. While most existing works first discretize the problem, we show that exact solutions of the infinite dimensional problem can be obtained by solving one or two consecutive finite dimensional convex programs depending on the measurement functions structures. We finish by showing an application on scattered data approximation. These results extend recent advances in the understanding of total-variation regularized inverse problems.

Estimates for Kuhn-Tucker points of perturbed convex programs

Optimization ◽  
1988 ◽  
Vol 19 (1) ◽  
pp. 29-43 ◽  
Author(s):  
R. Schultz
Keyword(s):  
Convex Programs

Strong duality for standard convex programs

2021 ◽  
Author(s):  
Kenneth O. Kortanek ◽  
Guolin Yu ◽  
Qinghong Zhang
Keyword(s):  
Strong Duality ◽  
Convex Programs

Shortfall Risk Models When Information on Loss Function Is Incomplete

2022 ◽  
Author(s):  
Erick Delage ◽  
Shaoyan Guo ◽  
Huifu Xu
Keyword(s):  
Partial Information ◽  
Risk Measures ◽  
Risk Attitude ◽  
Optimal Decision ◽  
Convex Programs ◽  
Risk Models ◽  
Shortfall Risk ◽  
Robust Version ◽  
Subjective Judgement ◽  
Optimal Decision Making

Utility-based shortfall risk measures effectively captures a decision maker's risk attitude on tail losses. In this paper, we consider a situation where the decision maker's risk attitude toward tail losses is ambiguous and introduce a robust version of shortfall risk, which mitigates the risk arising from such ambiguity. Specifically, we use some available partial information or subjective judgement to construct a set of plausible utility-based shortfall risk measures and define a so-called preference robust shortfall risk as through the worst risk that can be measured in this (ambiguity) set. We then apply the robust shortfall risk paradigm to optimal decision-making problems and demonstrate how the latter can be reformulated as tractable convex programs when the underlying exogenous uncertainty is discretely distributed.

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